Solve 3(x+7)-4(x+2)=x+5/2-x-1/3

$$3 ( x + 7 ) - 4 ( x + 2 ) = \frac { x + 5 } { 2 } - \frac { x - 1 } { 3 }$$

Solve for x

$$x = \frac{61}{7} = 8\frac{5}{7} \approx 8.714285714$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 6, the least common multiple of 2,3.

$$18\left(x+7\right)-24\left(x+2\right)=3\left(x+5\right)-2\left(x-1\right)$$

Use the distributive property to multiply 18 by x+7.

$$18x+126-24\left(x+2\right)=3\left(x+5\right)-2\left(x-1\right)$$

Use the distributive property to multiply -24 by x+2.

$$18x+126-24x-48=3\left(x+5\right)-2\left(x-1\right)$$

Combine 18x and -24x to get -6x.

$$-6x+126-48=3\left(x+5\right)-2\left(x-1\right)$$

Subtract 48 from 126 to get 78.

$$-6x+78=3\left(x+5\right)-2\left(x-1\right)$$

Use the distributive property to multiply 3 by x+5.

$$-6x+78=3x+15-2\left(x-1\right)$$

Use the distributive property to multiply -2 by x-1.

$$-6x+78=3x+15-2x+2$$

Combine 3x and -2x to get x.

$$-6x+78=x+15+2$$

Add 15 and 2 to get 17.

$$-6x+78=x+17$$

Subtract x from both sides.

$$-6x+78-x=17$$

Combine -6x and -x to get -7x.

$$-7x+78=17$$

Subtract 78 from both sides.

$$-7x=17-78$$

Subtract 78 from 17 to get -61.

$$-7x=-61$$

Divide both sides by -7.

$$x=\frac{-61}{-7}$$

Fraction \frac{-61}{-7} can be simplified to \frac{61}{7} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{61}{7}$$