Grade 7

Linear equations practice

Most linear equations are solved in three steps: move the terms, simplify, and divide by the coefficient.

Basic, Standard, Advanced: Grade 7 · Term 2

BasicStandardAdvancedMix

Moving terms

An equation stays true when the same number is added to, subtracted from, multiplied into or (if non-zero) divided into both sides. So a term may be moved to the other side if its sign is changed.

5x + 8 = 2x - 7 \;\to\; 3x = -15 \;\to\; x = -5

Check

Substitute the solution: both sides equal $-17$ .

Brackets, decimals and fractions

Brackets: expand first.
Decimals: multiply both sides by 10 or 100.
Fractions: multiply both sides by the LCM of the denominators, keeping numerators in brackets.

\frac{x + 4}{4} = \frac{3x + 9}{6} \;\to\; 3(x + 4) = 2(3x + 9) \;\to\; x = -2

Proportions

Property

a : b = c : d \;\Rightarrow\; ad = bc

Example: $(x - 2) : 3 = x : 5$ gives $5(x - 2) = 3x$ , so $x = 5$ .

Word problems

Choose what $x$ stands for.
Find two equal quantities and write an equation.
Solve it.
Check that the answer makes sense (for example, that a number of people is a whole number).

Q1BasicGr 7 · Term 2Linear equations

Solve the equation.

8x - 11 = -27

Answer

x = -2

Solution

Move the $x$ terms to the left and the numbers to the right.
$8x = -27 + 11$
Simplify both sides.
$8x = -16$
Divide both sides by $8$ .
$x = -2$

Q2StandardGr 7 · Term 2Linear equations

Solve the equation.

-1.4x + 0.5 = -0.6x + 1.3

Answer

x = -1

Solution

Multiply both sides by 10.
$-14x + 5 = -6x + 13$
Move the $x$ terms to the left and the numbers to the right.
$-14x + 6x = 13 - 5$
Simplify both sides.
$-8x = 8$
Divide both sides by $-8$ .
$x = -1$

Q3AdvancedGr 7 · Term 2Linear equations

You bought 12 items in total: pencils at 80 yen each and notebooks at 110 yen each. The total cost was 1080 yen. How many pencils did you buy?

Answer

8\text{ pencils}

Solution

Let $x$ be the number of pencils. From the total cost,
$80x + 110(12 - x) = 1080$
Expand and solve.
$80x + 1320 - 110x = 1080 \quad\to\quad -30x = -240 \quad\to\quad x = 8$
Then there are 4 notebooks, which fits the problem.
$80 \times 8 + 110 \times 4 = 1080$

Q1BasicGr 7 · Term 2Linear equations

Solve the equation.

5x - 13 = 8x - 10

Q2StandardGr 7 · Term 2Linear equations

Solve the equation.

\frac{x}{4} - 9 = \frac{x}{2} - 11

Q3AdvancedGr 7 · Term 2Linear equations

Candies are shared among some children. Giving 6 to each child leaves 6 over; giving 7 to each child leaves 8 short. Find the number of children and the number of candies.

Teleport

Main features

On this page

Topics

Display

Linear equations practice

Moving terms

Brackets, decimals and fractions

Proportions

Word problems

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Math problem generator

Moving terms

Brackets, decimals and fractions

Proportions

Word problems

Worked examples

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Practice problems

Hint

Answer

Solution

Hint

Answer

Solution

Hint

Answer

Solution

Related topics

Algebraic expressions

Direct and inverse proportion

Percentages and ratios