Solve 4(3x-1)-5(x+2)=7(2x+5)-(3x-16)

$$4 ( 3 x - 1 ) - 5 ( x + 2 ) = 7 ( 2 x + 5 ) - ( 3 x - 16 )$$

Solve for x

$$x = -\frac{65}{4} = -16\frac{1}{4} = -16.25$$

Steps for Solving Linear Equation

Use the distributive property to multiply 4 by 3x-1.

$$12x-4-5\left(x+2\right)=7\left(2x+5\right)-\left(3x-16\right)$$

Use the distributive property to multiply -5 by x+2.

$$12x-4-5x-10=7\left(2x+5\right)-\left(3x-16\right)$$

Combine 12x and -5x to get 7x.

$$7x-4-10=7\left(2x+5\right)-\left(3x-16\right)$$

Subtract 10 from -4 to get -14.

$$7x-14=7\left(2x+5\right)-\left(3x-16\right)$$

Use the distributive property to multiply 7 by 2x+5.

$$7x-14=14x+35-\left(3x-16\right)$$

To find the opposite of 3x-16, find the opposite of each term.

$$7x-14=14x+35-3x-\left(-16\right)$$

The opposite of -16 is 16.

$$7x-14=14x+35-3x+16$$

Combine 14x and -3x to get 11x.

$$7x-14=11x+35+16$$

Add 35 and 16 to get 51.

$$7x-14=11x+51$$

Subtract 11x from both sides.

$$7x-14-11x=51$$

Combine 7x and -11x to get -4x.

$$-4x-14=51$$

Add 14 to both sides.

$$-4x=51+14$$

Add 51 and 14 to get 65.

$$-4x=65$$

Divide both sides by -4.

$$x=\frac{65}{-4}$$

Fraction \frac{65}{-4} can be rewritten as -\frac{65}{4} by extracting the negative sign.

$$x=-\frac{65}{4}$$