Solve S=a+b/2*15

$$S = \frac { a + b } { 2 } \cdot 15$$

Solve for S

$$S=\frac{15\left(a+b\right)}{2}$$

Solution Steps

Express \frac{a+b}{2}\times 15 as a single fraction.

$$S=\frac{\left(a+b\right)\times 15}{2}$$

Use the distributive property to multiply a+b by 15.

$$S=\frac{15a+15b}{2}$$

Divide each term of 15a+15b by 2 to get \frac{15}{2}a+\frac{15}{2}b.

$$S=\frac{15}{2}a+\frac{15}{2}b$$

Solve for a

$$a=\frac{2S}{15}-b$$

Steps for Solving Linear Equation

Express \frac{a+b}{2}\times 15 as a single fraction.

$$S=\frac{\left(a+b\right)\times 15}{2}$$

Use the distributive property to multiply a+b by 15.

$$S=\frac{15a+15b}{2}$$

Divide each term of 15a+15b by 2 to get \frac{15}{2}a+\frac{15}{2}b.

$$S=\frac{15}{2}a+\frac{15}{2}b$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{15}{2}a+\frac{15}{2}b=S$$

Subtract \frac{15}{2}b from both sides.

$$\frac{15}{2}a=S-\frac{15}{2}b$$

The equation is in standard form.

$$\frac{15}{2}a=-\frac{15b}{2}+S$$

Divide both sides of the equation by \frac{15}{2}, which is the same as multiplying both sides by the reciprocal of the fraction.

$$\frac{\frac{15}{2}a}{\frac{15}{2}}=\frac{-\frac{15b}{2}+S}{\frac{15}{2}}$$

Dividing by \frac{15}{2} undoes the multiplication by \frac{15}{2}.

$$a=\frac{-\frac{15b}{2}+S}{\frac{15}{2}}$$

Divide S-\frac{15b}{2} by \frac{15}{2} by multiplying S-\frac{15b}{2} by the reciprocal of \frac{15}{2}.

$$a=\frac{2S}{15}-b$$