Solving Equations & Literal Equations — Challenge
Every step you take must keep the two sides equal. Say which property justifies it, and the algebra never drifts.
What these problems cover
These questions use 3 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Perimeter — Distance all the way around the outside.
- π — The circumference of any circle divided by its diameter — about 3.14159.
- Distribute — Multiply a bracket out: 3(x + 4) = 3x + 12.
Problem 1
Solve 5x=45.
- 5
- 9
- 40
- 50
- 225
Worked answer
9
Divide both sides by 5.
x = 455 = 9.
Check: 5(9) = 45.
Problem 2
Solve 3x+7=1.
- -2
- 2
- -3
- 3
- 8
Worked answer
-2
Subtract 7 from both sides: 3x = 1-7 = -6.
Divide by 3: x = -2.
Check: 3(-2)+7 = -6+7 = 1.
Problem 3
Solve x-12=-5.
- -17
- 7
- 17
- -7
- -60
Worked answer
7
Add 12 to both sides: x = -5+12.
-5+12 = 7.
Check: 7-12 = -5.
Problem 4
Solve 2(x-5)=3x.
- -10
- 10
- -2
- 2
- 5
Worked answer
-10
Expand the left side: 2x-10 = 3x.
Subtract 2x from both sides: -10 = x.
Check: 2(-10-5) = -30 and 3(-10) = -30, so both sides agree.
Problem 5
Solve x3-1=4.
- 9
- 12
- 15
- 18
- 5
Worked answer
15
Add 1 to both sides: x3 = 5.
Multiply by 3: x = 15.
Check: 153-1 = 5-1 = 4.
Problem 6
Solve -4x=20.
- -5
- 5
- -80
- 80
- -16
Worked answer
-5
Divide both sides by -4.
A positive divided by a negative is negative: x = 20-4 = -5.
Check: -4(-5) = 20.
Problem 7
Solve x+3.5=10.
- 6.5
- 13.5
- 7
- 3.5
- 35
Worked answer
6.5
Subtract 3.5 from both sides: x = 10-3.5.
10-3.5 = 6.5.
Check: 6.5+3.5 = 10.
Problem 8
Solve 6x-2=10.
- 1
- 2
- 3
- 4
- 12
Worked answer
2
Add 2 to both sides: 6x = 12.
Divide by 6: x = 2.
Check: 6(2)-2 = 10.