Algebra Questions with Answers and Solutions for Grade 8
Grade 8 algebra questions with solutions are presented. Questions on solving equations, simplifying expressions including expressions with fractions are included.
NOTE: In what follows, mixed numbers are written in the form a(b/c). For exampl 2 1/3 means the mixed number 2 + 1/3.
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Simplify the following algebraic expressions.
- -2x + 5 + 10x - 9
- 3(x + 7) + 2(-x + 4) + 5x
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Simplify the expressions.
- (2x - 6) / 2
- (-x - 2) / (x + 2)
- (5x - 5)/10
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Solve for x the following equations.
- -x = 6
- 2x - 8 = -x + 4
- 2x + 1/2 = 2/3
- x/3 + 2 = 5
- -5/x = 2
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Evaluate for the given values of x and y.
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x2 - y2 , for x = 4 and y = 5
- |4x - 2y| , for x = -2 and y = 3
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3x3 - 4y4 , for x = -1 and y = -2
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Solve the following inequalities.
- x + 6 < 0
- x + 1 > 5
- 2(x - 2) < 12
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What is the reciprocal of each of the following numbers?
- -1
- 0
- 3/4
- 2 5/7
- 0.02
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Evaluate the folwoing expressions involving mixed numbers.
- 3 3/4 + 6 1/7
- (1 3/5) × (3 1/3) - 2 1/2
- (5 2/3) ÷ (4 1/5)
- (3 4/7 - 1 1/2) ÷ (2 3/8 + 2 1/4)
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Evaluate the folwoing exponential expressions.
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-42
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(-2)3
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(-2)4
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10000
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5661
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Convert to fractions and write in simplest form.
- 0.02
- 12%
- 0.5%
- 1.12
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Convert to decimals.
- 1/5
- 120%
- 0.2%
- 4 8/5
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Convert to percent.
- 3/10
- 1.4
- 123.45
- 2 4/5
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Which of these numbers is divisible by 3?
- 156312
- 176314
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Which of these numbers is divisible by 4?
- 3432
- 1257
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Which of these numbers is divisible by 6?
- 1233
- 3432
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Which of these numbers is divisible by 9?
- 2538
- 1451
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Evaluate 8x + 7 given that x - 3 = 10.
Solutions and Answers to the Above Questions
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-2x + 5 + 10x - 9 : given
= (10x - 2x) + (5 - 9) : put like terms together
= 8x - 4 : group
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3(x + 7) + 2(-x + 4) + 5x : given
= 3x + 21 - 2x + 8 + 5x : expand
= (3x - 2x + 5x) + (21 + 8) : put like terms together
= 6x + 29 : group
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(2x - 6) / 2 : given
= 2(x - 3) / 2 : factor 2 in numerator
= x - 3 : divide numerator and denominator by 2 to simplify
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(-x - 2) / (x + 2) : given
= -1(x + 2) / (x + 2) : factor -1 in numerator
= -1 : divide numerator and denominator by x + 2 to simplify
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(5x - 5)/10 : given
= 5(x - 1) / 10 : factor 5 in numerator
= (x - 1) / 2 : divide numerator and denominator by 5 to simplify
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-x = 6 : given
x = -6 : multiply both sides of the equation by -1
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2x - 8 = -x + 4 : given
2x - 8 + 8 = -x + 4 + 8 : add +8 to both sides of the equation
2x = -x + 12 : group like terms
2x + x = -x + 12 + x : add +x to both sides
3x = 12 : group like terms
x = 4 : mutliply both sides by 1/3
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2x + 1/2 = 2/3 : given
2x + 1/2 - 1/2 = 2/3 - 1/2 : subtract 1/2 from both sides
2x = 1/6 : group like terms
x = 1/12 : multiply both sides by 1/2
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x/3 + 2 = 5 : given
x/3 + 2 - 2 = 5 - 2 : subtract 2 from both sides
x/3 = 3 : group like terms
x = 9 : multiply both sides by 1/2
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-5/x = 2 : given
-5 = 2x : multiply both sides by x and simplify
-5/2 = x : : multiply both sides by 1/2
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x2 - y2 , x = 4 , y = 5 : given
42 - 52 : substitute x and y by the given values
=16 - 25 = -9
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|4x - 2y| , x = -2 , y = 3 : given
|4(-2) - 2(3)| : substitute x and y by the given values
= |-14| = 14 : evaluate
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3x3 - 4y4 , x = -1 , y = -2 : given
3(-1)3 - 4(-2)4 : substitute x and y by the given values
= -3 - 64 = -67 : evaluate
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x + 6 < 0 : given
x + 6 - 6 < -6 : subtract 6 from both sides
x < -6 : group like terms
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x + 1 > 5 : given
x + 1 - 1 > 5 - 1 : subtract 1 from both sides
x > 4 : group like terms
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2(x - 2) < 12 : given
x - 2 < 6 : mutliply both sides by 1/2
x - 2 + 2 < 6 + 2 : add 2 to both sides
x < 8 : group like terms
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(-1) a = 1 : definition: a is the reciprocal of -1
a = 1/-1 = -1 : solve for a; -1 is the reciprocal of -1
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(0) b = 1 : definition: b is the reciprocal of 0
b = undefined : no value of b satisfies the above equation
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(3/4) c = 1 : definition: c is the reciprocal of 3/4
c = 4/3 : solve for c; c = 4/3 is the reciprocal of 3/4
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(2 5/7) d = 1 : definition: d is the reciprocal of 2 5/7.
(19/7) d = 1 : convert the mixed number 2 5/7 into a fraction.
d = 7/19 : : solve for d; d = 7/19 is the reciprocal of 2(5/7)
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0.02 d = 1 : definition: d is the reciprocal of 0.02.
d = 1/0.02 : solve for d; d = 50 is the reciprocal of 0.02
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3 3/4 + 6 1/7 : given
= (3 + 6) + (3/4 + 1/7) : put the whole parts together and the fractional parts together.
= 9 + (21/28 + 4/28) : add.
= 9 25/28
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(1 3/5) × (3 1/3) - 2 1/2 : given
= (8/5) × (10/3) - 2 1/2 : convert mixed numbers to mupliply into fractions.
= 80/15 - 2 1/2 = 5 1/3 - 2 1/2 = 4 4/3 - 2 1/2: mupliply and write as mixed number if possible
= (4 - 2) + (4/3 - 1/2) : subtract
= 2 5/6
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(5 2/3) ÷ (4 1/5) : given
= (17/3) ÷ (21/5) : convert mixed numbers to fractions.
= 85 / 63 : divide fractions
= 1 22/63 : write as mixed number
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(3 4/7 - 1 1/2) ÷ (2 3/8 + 2 1/4) : given
= [(3 - 1) + (4/7 - 1/2)] ÷ [(2 + 2) + (3/8 + 1/4)]: evaluate numerator and denominator as fractions.
= (2 1/14) ÷ (4 5/8)
= (29/14) ÷ (37/8)
= 116/259
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-42 : given
= - (4 × 4) = -16 : expand and calculate
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(-2)3 : given
= (-2)×(-2)×(-2) = -8 : expand and calculate
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10000 : given
= 10000 = 1 : definition: any nonzero number to the power zero gives 1
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5661 : given
= 5661 = 566
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- 0.02 = 1/50
- 12% = 3/25
- 0.5% = 1/200
- 1.12 = 28/25
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- 1/5 = 0.2
- 120% = 1.2
- 0.2% = 0.002
- 4 8/5 = 5.6
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- 3/10 = 30%
- 1.4 = 140%
- 123.45 = 12345%
- 2 4/5 = 280%
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- 156312 , is divisible by 3
- 176314 , is not divisible by 3
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- 3432 , is divisible by 4
- 1257 , is not divisible by 4
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- 1233 , is not divisible by 6
- 3432 , is divisible by 6
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- 2538 , is divisible by 9
- 1451 , is not divisible by 9
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Evaluate 8x + 7 given that x - 3 = 10.
x - 3 = 10: given equation
x = 10 + 3 = 13: solve the givenequation.
8(13) + 7 = 111 substitute x by 3 in the given expression and evaluate.
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Updated: 20 May 2009 (A Dendane)