Simplify 23 - 7(1-x) = 26 - 5(2-4x) - 13x

Answer 1

The key here is to follow the order of operations and start by distributing the -7 and -5 through multiplication. (Be sure to keep track of the negatives!) Then, combine like terms and simplify:

23 - 7(1 - x) = 26 - 5(2 - 4x) - 13x

23 - 7 + 7x = 26 - 10 + 20x - 13x

16 + 7x = 16 + 7x

Since both sides of the equation match, that means that any value of x can satisfy the equation and your answer is "x = all real numbers".

Answer 2

This is an equation. We do not simplify equations, we solve them.

Each side of the equation can be simplified separately.

Left side:

23 - 7(1 - x)

= 23 - 7 + 7x

= 16 + 7x.

Right side:

26 - 5(2 - 4x) - 13x

= 26 - 10 + 20x - 13x

= 16 + 7x.

We see that left and right side simplify to the same expression, (16 + 7x).

Equation like this, that left and right side simplify to the same expression are called identities.

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