Solve 1/2(x+6)=2xtext{and}5-2x=7x-h

$$\frac { 1 } { 2 } ( x + 6 ) = 2 x \text { and } 5 - 2 x = 7 x - h$$

Solve for x, h

$$x=2$$

$$h=13$$

Solution Steps

Consider the first equation. Use the distributive property to multiply \frac{1}{2} by x+6.

$$\frac{1}{2}x+3=2x$$

Subtract 2x from both sides.

$$\frac{1}{2}x+3-2x=0$$

Combine \frac{1}{2}x and -2x to get -\frac{3}{2}x.

$$-\frac{3}{2}x+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$-\frac{3}{2}x=-3$$

Multiply both sides by -\frac{2}{3}, the reciprocal of -\frac{3}{2}.

$$x=-3\left(-\frac{2}{3}\right)$$

Multiply -3 and -\frac{2}{3} to get 2.

$$x=2$$

Consider the second equation. Insert the known values of variables into the equation.

$$5-2\times 2=7\times 2-h$$

Multiply -2 and 2 to get -4.

$$5-4=7\times 2-h$$

Subtract 4 from 5 to get 1.

$$1=7\times 2-h$$

Multiply 7 and 2 to get 14.

$$1=14-h$$

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

$$14-h=1$$

Subtract 14 from both sides.

$$-h=1-14$$

Subtract 14 from 1 to get -13.

$$-h=-13$$

Divide both sides by -1.

$$h=\frac{-13}{-1}$$

Fraction \frac{-13}{-1} can be simplified to 13 by removing the negative sign from both the numerator and the denominator.

$$h=13$$

The system is now solved.

$$x=2 h=13$$