Solve 6x − 7 = −31

The solution of 6x − 7 = −31 is x = -4.

6x - 7 = -31\ \Rightarrow\ x = -4

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The lines y = 6x − 7 and y = -31 meet at x = -4. 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.
$6x - 7 = -31$
2
Add 7 to both sides:
$6x - 7 + 7 = -31 + 7 \ \Rightarrow\ 6x = -24$
3
Divide both sides by 6:
$\frac{6x}{6} = \frac{-24}{6} \ \Rightarrow\ x = -4$
4
Check: put x = -4 back into the equation.
$6\cdot(-4) - 7 = -24 - 7 = -31 \checkmark$

LaTeX source of the formulas on this page

\[ 6x - 7 = -31\ \Rightarrow\ x = -4 \]
\[ 6x - 7 = -31 \]
\[ 6x - 7 + 7 = -31 + 7 \ \Rightarrow\ 6x = -24 \]
\[ \frac{6x}{6} = \frac{-24}{6} \ \Rightarrow\ x = -4 \]
\[ 6\cdot(-4) - 7 = -24 - 7 = -31 \checkmark \]

Trying values of x in 6x − 7 = −31

x	6x − 7	Equals -31?
-6	-43	no
-5	-37	no
-4	-31	yes
-3	-25	no
-2	-19	no

Questions

What is x in 6x − 7 = −31?

The solution of 6x − 7 = −31 is x = -4.

How do you solve 6x − 7 = −31?

Add 7 to both sides to get 6x = -24, then divide both sides by 6 to get x = -4.

How do I check the answer?

Replace x by -4: 6(-4) − 7 = -31, which is -31.

Solve 6x − 7 = −31

How to work it out

Trying values of x in 6x − 7 = −31

Questions

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