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Algebra · Guided Practice

Linear Equations

14 questions with answers and video solutions. Try each one before revealing the answer.

1
Solve: 3x−2=5\displaystyle 3x-2=5
2
Solve: 9−4a=1\displaystyle 9-4a=1
3
Solve: 7t+8=32−5t\displaystyle 7t+8=32-5t
4
Solve: 4n−3=3(3n−2)\displaystyle 4n-3=3(3n-2)
5
Solve: x3−2=x\displaystyle \large\frac{x}{3}\normalsize -2 = x
6
Solve: x−23=2x+12\displaystyle \large\frac{x-2}{3}\normalsize = \large\frac{2x+1}{2}\normalsize
7
Solve
x+25=−3x4\displaystyle \large\frac{x+2}{5}\normalsize = -\large\frac{3x}{4}\normalsize
8
Solve
56a−2=3a+48\displaystyle \large\frac{5}{6}\normalsize a-2=\large\frac{3a+4}{8}\normalsize
9
Solve
6−2(3x−5)=−10x\displaystyle 6-2(3x-5)=-10x
10
2016 P1 Q8
3 Marks

Solve the equation 2x3−56=2x\displaystyle \frac{2x}{3}-\frac{5}{6}=2x.
Give your answer in its simplest form.

11
2017 P1 Q15
3 Marks

In the diagram:
TS is parallel to QR.
TS = 5 cm, QR = 7 cm, SR = 2.6 cm.
The length of PS is x\displaystyle x cm.

Similar triangles

Calculate the value of x.\displaystyle x.

12
2019 P1 Q14
3 Marks

Solve the equation x2−1=3−x5.\displaystyle \frac{x}{2}-1=\frac{3-x}{5}.

13
2022 P1 Q15
(1, 4)5 Marks

A triangle and rectangle are shown in the diagram.

Triangle and rectangle diagram

(a)  Find an expression for the area of the triangle.

(b)  Given that the area of the triangle is equal to the area of the rectangle, find algebraically the value of x\displaystyle x.

14
2025 P2 Q13
3 Marks

Solve the equation 5x+12=4x3+1.\displaystyle \frac{5x+1}{2}=\frac{4x}{3}+1.

Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.

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