Solve 12x − 13 = 83

The solution of 12x − 13 = 83 is x = 8.

12x - 13 = 83\ \Rightarrow\ x = 8

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The lines y = 12x − 13 and y = 83 meet at x = 8. The solution of the equation is the x-coordinate of the point where the two sides are equal.

How to work it out

1
The goal is to get x alone. Undo the operations in the opposite order: first the subtraction, then the multiplication.
$12x - 13 = 83$
2
Add 13 to both sides:
$12x - 13 + 13 = 83 + 13 \ \Rightarrow\ 12x = 96$
3
Divide both sides by 12:
$\frac{12x}{12} = \frac{96}{12} \ \Rightarrow\ x = 8$
4
Check: put x = 8 back into the equation.
$12\cdot8 - 13 = 96 - 13 = 83 \checkmark$

LaTeX source of the formulas on this page

\[ 12x - 13 = 83\ \Rightarrow\ x = 8 \]
\[ 12x - 13 = 83 \]
\[ 12x - 13 + 13 = 83 + 13 \ \Rightarrow\ 12x = 96 \]
\[ \frac{12x}{12} = \frac{96}{12} \ \Rightarrow\ x = 8 \]
\[ 12\cdot8 - 13 = 96 - 13 = 83 \checkmark \]

Trying values of x in 12x − 13 = 83

x	12x − 13	Equals 83?
6	59	no
7	71	no
8	83	yes
9	95	no
10	107	no

Questions

What is x in 12x − 13 = 83?

The solution of 12x − 13 = 83 is x = 8.

How do you solve 12x − 13 = 83?

Add 13 to both sides to get 12x = 96, then divide both sides by 12 to get x = 8.

How do I check the answer?

Replace x by 8: 12(8) − 13 = 83, which is 83.

Solve 12x − 13 = 83

How to work it out

Trying values of x in 12x − 13 = 83

Questions

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