7th Grade Math · Unit 4
Undo addition or subtraction, then multiply or divide.
Keep the balance
An equation is a balance. Do the same move on both sides.
If you subtract a number on the left, subtract it on the right too.
Undo addition or subtraction first
If a number is added to the variable term, subtract it from both sides. If a number is subtracted, add it to both sides.
That leaves the variable term alone.
Then multiply or divide
Divide both sides by the coefficient, or multiply both sides by its reciprocal.
From 2x + 3 = 11, subtract 3, then divide by 2.
The coefficient and the added number are positive whole numbers.
2x + 3 = 11
2x + 3 − 3 = 11 − 3
2x = 8
Divide both sides by 2.
x = 4
Answer: x = 4
3x + 4 = 19
3x + 4 − 4 = 19 − 4
3x = 15
Divide both sides by 3.
x = 5
Answer: x = 5
4x + 5 = 29
4x + 5 − 5 = 29 − 5
4x = 24
Divide both sides by 4.
x = 6
Answer: x = 6
5x + 2 = 27
5x + 2 − 2 = 27 − 2
5x = 25
Divide both sides by 5.
x = 5
Answer: x = 5
2x + 7 = 21
2x + 7 − 7 = 21 − 7
2x = 14
Divide both sides by 2.
x = 7
Answer: x = 7
3x + 5 = 26
3x + 5 − 5 = 26 − 5
3x = 21
Divide both sides by 3.
x = 7
Answer: x = 7
4x + 1 = 21
4x + 1 − 1 = 21 − 1
4x = 20
Divide both sides by 4.
x = 5
Answer: x = 5
6x + 3 = 27
6x + 3 − 3 = 27 − 3
6x = 24
Divide both sides by 6.
x = 4
Answer: x = 4
2x + 9 = 25
2x + 9 − 9 = 25 − 9
2x = 16
Divide both sides by 2.
x = 8
Answer: x = 8
3x + 8 = 23
3x + 8 − 8 = 23 − 8
3x = 15
Divide both sides by 3.
x = 5
Answer: x = 5
5x + 6 = 31
5x + 6 − 6 = 31 − 6
5x = 25
Divide both sides by 5.
x = 5
Answer: x = 5
The coefficient may be a fraction, or the equation may subtract.
12x + 3 = 8
12x + 3 − 3 = 8 − 3
12x = 5
Multiply both sides by 2.
x = 10
Answer: x = 10
23x + 1 = 5
23x + 1 − 1 = 5 − 1
23x = 4
Multiply both sides by 32.
x = 6
Answer: x = 6
34x + 2 = 8
34x + 2 − 2 = 8 − 2
34x = 6
Multiply both sides by 43.
x = 8
Answer: x = 8
13x + 2 = 6
13x + 2 − 2 = 6 − 2
13x = 4
Multiply both sides by 3.
x = 12
Answer: x = 12
32x + 1 = 10
32x + 1 − 1 = 10 − 1
32x = 9
Multiply both sides by 23.
x = 6
Answer: x = 6
25x + 3 = 7
25x + 3 − 3 = 7 − 3
25x = 4
Multiply both sides by 52.
x = 10
Answer: x = 10
2x − 3 = 11
2x − 3 + 3 = 11 + 3
2x = 14
Divide both sides by 2.
x = 7
Answer: x = 7
3x − 4 = 11
3x − 4 + 4 = 11 + 4
3x = 15
Divide both sides by 3.
x = 5
Answer: x = 5
5x − 2 = 18
5x − 2 + 2 = 18 + 2
5x = 20
Divide both sides by 5.
x = 4
Answer: x = 4
2x − 3 = 4
2x − 3 + 3 = 4 + 3
2x = 7
Divide both sides by 2.
x = 72
Answer: x = 72
3x − 1 = 3
3x − 1 + 1 = 3 + 1
3x = 4
Divide both sides by 3.
x = 43
Answer: x = 43
The coefficient is negative.
−2x + 8 = 2
−2x + 8 − 8 = 2 − 8
−2x = −6
Divide both sides by −2.
x = 3
Answer: x = 3
−3x + 12 = 3
−3x + 12 − 12 = 3 − 12
−3x = −9
Divide both sides by −3.
x = 3
Answer: x = 3
−4x + 10 = −6
−4x + 10 − 10 = −6 − 10
−4x = −16
Divide both sides by −4.
x = 4
Answer: x = 4
−5x + 20 = 5
−5x + 20 − 20 = 5 − 20
−5x = −15
Divide both sides by −5.
x = 3
Answer: x = 3
−2x + 5 = 15
−2x + 5 − 5 = 15 − 5
−2x = 10
Divide both sides by −2.
x = −5
Answer: x = −5
−3x + 4 = −8
−3x + 4 − 4 = −8 − 4
−3x = −12
Divide both sides by −3.
x = 4
Answer: x = 4
−6x + 9 = −3
−6x + 9 − 9 = −3 − 9
−6x = −12
Divide both sides by −6.
x = 2
Answer: x = 2
−12x + 5 = 1
−12x + 5 − 5 = 1 − 5
−12x = −4
Multiply both sides by −2.
x = 8
Answer: x = 8
−23x + 4 = 0
−23x + 4 − 4 = 0 − 4
−23x = −4
Multiply both sides by −32.
x = 6
Answer: x = 6
−34x + 6 = 0
−34x + 6 − 6 = 0 − 6
−34x = −6
Multiply both sides by −43.
x = 8
Answer: x = 8
−32x + 9 = 3
−32x + 9 − 9 = 3 − 9
−32x = −6
Multiply both sides by −23.
x = 4
Answer: x = 4
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