Solve 7+2(3(x+1)-2(3x-1)-(4x-3))

$$7+2(3(x+1)-2(3x-1)-(4x-3))$$

Evaluate

$$23-14x$$

Solution Steps

Use the distributive property to multiply 3 by x+1.

$$7+2\left(3x+3-2\left(3x-1\right)-\left(4x-3\right)\right)$$

Use the distributive property to multiply -2 by 3x-1.

$$7+2\left(3x+3-6x+2-\left(4x-3\right)\right)$$

Combine 3x and -6x to get -3x.

$$7+2\left(-3x+3+2-\left(4x-3\right)\right)$$

Add 3 and 2 to get 5.

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

To find the opposite of 4x-3, find the opposite of each term.

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

The opposite of -3 is 3.

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

Combine -3x and -4x to get -7x.

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

Add 5 and 3 to get 8.

$$7+2\left(-7x+8\right)$$

Use the distributive property to multiply 2 by -7x+8.

$$7-14x+16$$

Add 7 and 16 to get 23.

$$23-14x$$

Expand

$$23-14x$$

Solution Steps

Use the distributive property to multiply 3 by x+1.

$$7+2\left(3x+3-2\left(3x-1\right)-\left(4x-3\right)\right)$$

Use the distributive property to multiply -2 by 3x-1.

$$7+2\left(3x+3-6x+2-\left(4x-3\right)\right)$$

Combine 3x and -6x to get -3x.

$$7+2\left(-3x+3+2-\left(4x-3\right)\right)$$

Add 3 and 2 to get 5.

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

To find the opposite of 4x-3, find the opposite of each term.

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

The opposite of -3 is 3.

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

Combine -3x and -4x to get -7x.

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

Add 5 and 3 to get 8.

$$7+2\left(-7x+8\right)$$

Use the distributive property to multiply 2 by -7x+8.

$$7-14x+16$$

Add 7 and 16 to get 23.

$$23-14x$$