Solve 10x − 1 = 109

The solution of 10x − 1 = 109 is x = 11.

10x - 1 = 109\ \Rightarrow\ x = 11

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The lines y = 10x − 1 and y = 109 meet at x = 11. 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.
$10x - 1 = 109$
2
Add 1 to both sides:
$10x - 1 + 1 = 109 + 1 \ \Rightarrow\ 10x = 110$
3
Divide both sides by 10:
$\frac{10x}{10} = \frac{110}{10} \ \Rightarrow\ x = 11$
4
Check: put x = 11 back into the equation.
$10\cdot11 - 1 = 110 - 1 = 109 \checkmark$

LaTeX source of the formulas on this page

\[ 10x - 1 = 109\ \Rightarrow\ x = 11 \]
\[ 10x - 1 = 109 \]
\[ 10x - 1 + 1 = 109 + 1 \ \Rightarrow\ 10x = 110 \]
\[ \frac{10x}{10} = \frac{110}{10} \ \Rightarrow\ x = 11 \]
\[ 10\cdot11 - 1 = 110 - 1 = 109 \checkmark \]

Trying values of x in 10x − 1 = 109

x	10x − 1	Equals 109?
9	89	no
10	99	no
11	109	yes
12	119	no
13	129	no

Questions

What is x in 10x − 1 = 109?

The solution of 10x − 1 = 109 is x = 11.

How do you solve 10x − 1 = 109?

Add 1 to both sides to get 10x = 110, then divide both sides by 10 to get x = 11.

How do I check the answer?

Replace x by 11: 10(11) − 1 = 109, which is 109.

Solve 10x − 1 = 109

How to work it out

Trying values of x in 10x − 1 = 109

Questions

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