Solve 7(3x-8)-[4x-(3-x)]=46x-1-3(x+2)

$$7 ( 3 x - 8 ) - [ 4 x - ( 3 - x ) ] = 46 x - 1 - 3 ( x + 2 )$$

Solve for x

$$x = -\frac{46}{27} = -1\frac{19}{27} \approx -1.703703704$$

Steps for Solving Linear Equation

Use the distributive property to multiply 7 by 3x-8.

$$21x-56-\left(4x-\left(3-x\right)\right)=46x-1-3\left(x+2\right)$$

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

$$21x-56-\left(4x-3-\left(-x\right)\right)=46x-1-3\left(x+2\right)$$

The opposite of -x is x.

$$21x-56-\left(4x-3+x\right)=46x-1-3\left(x+2\right)$$

Combine 4x and x to get 5x.

$$21x-56-\left(5x-3\right)=46x-1-3\left(x+2\right)$$

To find the opposite of 5x-3, find the opposite of each term.

$$21x-56-5x-\left(-3\right)=46x-1-3\left(x+2\right)$$

The opposite of -3 is 3.

$$21x-56-5x+3=46x-1-3\left(x+2\right)$$

Combine 21x and -5x to get 16x.

$$16x-56+3=46x-1-3\left(x+2\right)$$

Add -56 and 3 to get -53.

$$16x-53=46x-1-3\left(x+2\right)$$

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

$$16x-53=46x-1-3x-6$$

Combine 46x and -3x to get 43x.

$$16x-53=43x-1-6$$

Subtract 6 from -1 to get -7.

$$16x-53=43x-7$$

Subtract 43x from both sides.

$$16x-53-43x=-7$$

Combine 16x and -43x to get -27x.

$$-27x-53=-7$$

Add 53 to both sides.

$$-27x=-7+53$$

Add -7 and 53 to get 46.

$$-27x=46$$

Divide both sides by -27.

$$x=\frac{46}{-27}$$

Fraction \frac{46}{-27} can be rewritten as -\frac{46}{27} by extracting the negative sign.

$$x=-\frac{46}{27}$$