Arithmetic with Expressions: Additional Practice (Set 2)

Work from the inside out, flipping signs after each minus.

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

Then $8x - (4x + 8) = 4x - 8$.

Distribute each minus sign, then combine like terms.

$(4a - 5) - (a - 2) - (a + 1) = 4a - 5 - a + 2 - a - 1 = 2a - 4$

Distribute the minus and combine, then substitute $x = 2$.

$(5x - 2) - (2x - 6) = 3x + 4, \quad 3(2) + 4 = 10$

Clear the innermost parentheses first.

$2x - (x - 5) = x + 5, \quad 3(x + 5) = 3x + 15$

Then $3x + 15 - 4x = -x + 15$.

Distribute both products, then combine like terms.

$3(a - 2b) - 2(2a - b) = 3a - 6b - 4a + 2b = -a - 4b$

Simplify first, then substitute $x = 3$.

$4(x - 2) - 2(x - 5) = 2x + 2, \quad 2(3) + 2 = 8$

Simplify first, then substitute $x = -1$.

$3(2x - 1) - (4x - 5) = 2x + 2, \quad 2(-1) + 2 = 0$

Distribute the leading minus, then combine.

$-(3x - 2) + (x - 5) = -3x + 2 + x - 5 = -2x - 3$

Group the $x^2$ terms, the $x$ terms, and the constants.

$x^2 - 2x^2 = -x^2, \quad 3x + x = 4x, \quad -5 + 8 = 3$

The result is $-x^2 + 4x + 3$.

Distribute both products, watching the signs.

$-2(3 - x) - 3(x - 4) = -6 + 2x - 3x + 12 = -x + 6$

Distribute all three groups, then combine like terms.

$2(3a - b) - 3(a - 2b) - (a + b) = 6a - 2b - 3a + 6b - a - b = 2a + 3b$

Simplify first, then substitute $a = 3$ and $b = -1$.

$2(a + b) - (a - b) = a + 3b, \quad 3 + 3(-1) = 0$