Solve \( 3x + 7 = 22 \).
\( 3x = 15 \) ⇒ \( x = 5 \).
Equations & Inequalities
10 exam-style questions on linear equations, simultaneous equations and inequalities.
3 Easy 4 Medium 3 Hard
Solve \( 5x - 2 = 3x + 8 \).
\( 2x = 10 \) ⇒ \( x = 5 \).
Solve the inequality \( 2x + 3 < 11 \).
\( 2x < 8 \) ⇒ \( x < 4 \).
Solve \( \dfrac{x+1}{3} = \dfrac{x-2}{2} \).
\( 2(x+1) = 3(x-2) \) ⇒ \( 2x + 2 = 3x - 6 \) ⇒ \( x = 8 \).
Solve the simultaneous equations: \( x + y = 10 \), \( 2x - y = 5 \).
Add: \( 3x = 15 \) ⇒ \( x = 5 \). Then \( y = 5 \).
Solve \( 3(x - 2) = 2(x + 5) \).
\( 3x - 6 = 2x + 10 \) ⇒ \( x = 16 \).
Solve \( -2 < 3x + 1 \leq 10 \) and represent the solution on a number line (describe the solution set).
\( -3 < 3x \leq 9 \) ⇒ \( -1 < x \leq 3 \). Open circle at \( -1 \), closed at \( 3 \).
Solve the simultaneous equations: \( 2x + 3y = 13 \), \( 3x - y = 3 \).
From second: \( y = 3x - 3 \). Sub: \( 2x + 3(3x-3) = 13 \) ⇒ \( 2x + 9x - 9 = 13 \) ⇒ \( 11x = 22 \) ⇒ \( x = 2 \), \( y = 3 \).
The perimeter of a rectangle is \( 54 \) cm. The length is \( 3 \) cm more than twice the width. Find the dimensions.
Let width \( = w \). Length \( = 2w + 3 \). \( 2(w + 2w + 3) = 54 \) ⇒ \( 6w + 6 = 54 \) ⇒ \( w = 8 \). Length \( = 19 \) cm.
Solve \( \dfrac{2x-1}{4} - \dfrac{x+3}{3} = 1 \).
Multiply through by \( 12 \): \( 3(2x-1) - 4(x+3) = 12 \) ⇒ \( 6x - 3 - 4x - 12 = 12 \) ⇒ \( 2x - 15 = 12 \) ⇒ \( 2x = 27 \) ⇒ \( x = 13.5 \).