Solutions to Matched Exercises in Algebra Tutorial

The solutions to all the matched exercises in algebra tutorial page are presented.

Matched Exercise 1 Simplify the expression

\[ 2(a - 8b) - (5 - b) + b + (6b - 9) - a \]

Solution to Exercise 1

a - 8b -14

Matched Exercise 2: Solve the equation

\[ 2(-x - 5) - (-6 + x) = -3(2x + 4) + 12 \]

Solution to Exercise 2

\(x = \frac{4}{3}\)

Matched Exercise 3: If \(x > 3\), simplify the expression

\[ 2| x - 3 | + 6x - (2 - 3x) + | 9 - 20 | \]

Solution to Exercise 3

\(11x + 3\)

Matched Exercise 4: Find the slope and the y-intercept of the line given by the equation

\[ -3y - 6x = 7 \]

Solution to Exercise 4

slope = -2
y intercept at \((0 , -\frac{7}{3})\)

Matched Exercise 5: Find the equation of the line passing through the points \((0 , 3)\) and \((-1 , 1)\).

Solution to Exercise 5

\(y = 2x + 3\)

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