Arithmetic with Expressions: Practice

Distribute both leading minus signs, then combine.

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

Distribute each product, watching the sign of the second one.

$3(2x - 1) - 2(x - 4) = 6x - 3 - 2x + 8 = 4x + 5$

Combine the $x^2$ terms and the $xy$ terms separately.

$4x^2 + x^2 = 5x^2, \quad -3xy + 5xy = 2xy$

The result is $5x^2 + 2xy$.

Expand each. The first three all give $6x - 9$, but the last does not.

$3(2x - 9) = 6x - 27 \neq 6x - 9$

Clear the innermost parentheses first.

$3 - (x - 1) = 4 - x, \quad -2(4 - x) = -8 + 2x$

Then $5 - 8 + 2x = 2x - 3$.

The $x$ term is $-x$, which is $-1x$.

$-x = -1x$

So its coefficient is $-1$.

Work from the inside out.

$2x - (3 - x) = 3x - 3, \quad x - (3x - 3) = -2x + 3$

Distribute, mind the minus, then combine the $x^2$ and $x$ terms.

$2(x^2 + 3x) - (x^2 - x) = 2x^2 + 6x - x^2 + x = x^2 + 7x$

Substitute each value into both expressions. Only at $x = 1$ do they agree.

$3(1) + 5 = 8, \quad 8(1) = 8$

At every other value the two expressions differ, so $x = 1$ is the coincidence that does not expose the error.

Clear the brackets from the inside out.

$x - 2(x - 1) = -x + 2, \quad 4(-x + 2) = -4x + 8$

Then $-4x + 8 + 3x = -x + 8$.

Distribute the minus, then combine the $m$ terms and the $n$ terms.

$5m - 2n - (3m - 4n) + n = 5m - 2n - 3m + 4n + n = 2m + 3n$

Distribute both minus signs and combine.

$-(a - b) - (b - a) = -a + b - b + a = 0$

Every term cancels.