Solve x=260-150+0.1/2*(150+x)

$$x = 260 - 150 + \frac { 0.1 } { 2 } \cdot ( 150 + x )$$

Solve for x

$$x = \frac{2350}{19} = 123\frac{13}{19} \approx 123.684210526$$

Steps for Solving Linear Equation

Subtract 150 from 260 to get 110.

$$x=110+\frac{0.1}{2}\left(150+x\right)$$

Expand \frac{0.1}{2} by multiplying both numerator and the denominator by 10.

$$x=110+\frac{1}{20}\left(150+x\right)$$

Use the distributive property to multiply \frac{1}{20} by 150+x.

$$x=110+\frac{1}{20}\times 150+\frac{1}{20}x$$

Multiply \frac{1}{20} and 150 to get \frac{150}{20}.

$$x=110+\frac{150}{20}+\frac{1}{20}x$$

Reduce the fraction \frac{150}{20} to lowest terms by extracting and canceling out 10.

$$x=110+\frac{15}{2}+\frac{1}{20}x$$

Convert 110 to fraction \frac{220}{2}.

$$x=\frac{220}{2}+\frac{15}{2}+\frac{1}{20}x$$

Since \frac{220}{2} and \frac{15}{2} have the same denominator, add them by adding their numerators.

$$x=\frac{220+15}{2}+\frac{1}{20}x$$

Add 220 and 15 to get 235.

$$x=\frac{235}{2}+\frac{1}{20}x$$

Subtract \frac{1}{20}x from both sides.

$$x-\frac{1}{20}x=\frac{235}{2}$$

Combine x and -\frac{1}{20}x to get \frac{19}{20}x.

$$\frac{19}{20}x=\frac{235}{2}$$

Multiply both sides by \frac{20}{19}, the reciprocal of \frac{19}{20}.

$$x=\frac{235}{2}\times \frac{20}{19}$$

Multiply \frac{235}{2} times \frac{20}{19} by multiplying numerator times numerator and denominator times denominator.

$$x=\frac{235\times 20}{2\times 19}$$

Do the multiplications in the fraction \frac{235\times 20}{2\times 19}.

$$x=\frac{4700}{38}$$

Reduce the fraction \frac{4700}{38} to lowest terms by extracting and canceling out 2.

$$x=\frac{2350}{19}$$