Solve 7x − 5 = −75

The solution of 7x − 5 = −75 is x = -10.

7x - 5 = -75\ \Rightarrow\ x = -10

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The lines y = 7x − 5 and y = -75 meet at x = -10. 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.
$7x - 5 = -75$
2
Add 5 to both sides:
$7x - 5 + 5 = -75 + 5 \ \Rightarrow\ 7x = -70$
3
Divide both sides by 7:
$\frac{7x}{7} = \frac{-70}{7} \ \Rightarrow\ x = -10$
4
Check: put x = -10 back into the equation.
$7\cdot(-10) - 5 = -70 - 5 = -75 \checkmark$

LaTeX source of the formulas on this page

\[ 7x - 5 = -75\ \Rightarrow\ x = -10 \]
\[ 7x - 5 = -75 \]
\[ 7x - 5 + 5 = -75 + 5 \ \Rightarrow\ 7x = -70 \]
\[ \frac{7x}{7} = \frac{-70}{7} \ \Rightarrow\ x = -10 \]
\[ 7\cdot(-10) - 5 = -70 - 5 = -75 \checkmark \]

Trying values of x in 7x − 5 = −75

x	7x − 5	Equals -75?
-12	-89	no
-11	-82	no
-10	-75	yes
-9	-68	no
-8	-61	no

Questions

What is x in 7x − 5 = −75?

The solution of 7x − 5 = −75 is x = -10.

How do you solve 7x − 5 = −75?

Add 5 to both sides to get 7x = -70, then divide both sides by 7 to get x = -10.

How do I check the answer?

Replace x by -10: 7(-10) − 5 = -75, which is -75.

Solve 7x − 5 = −75

How to work it out

Trying values of x in 7x − 5 = −75

Questions

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