Question

name:
simplify:

1. $16\div(4 - 2)-3$ 2. $7x + 5(1 - x)$ 3. $(-2)(-y)$

solve:

1. $5 + 2n = 12$ 5. $4y - 7 = 3y - 4$ 6. $6x - 7 = x + 8$
2. $\frac{x}{2}=14$ 8. $14x + 3x - 40 = 11$ 9. $|x| = 6$
3. write the expression for: ten less than a number(x).
4. rewrite the following numbers, least to greatest. $4.12, - 3.68, 1.22, - 4.33, 2\frac{2}{3}, - 2\frac{2}{5}$
5. what quadrant is the point $(-4, - 8)$ located ?

Explanation:

Step1: Simplify inside parentheses first

$16\div(4-2)-3 = 16\div2-3$

Step2: Perform division operation

$16\div2-3 = 8-3$

Step3: Perform subtraction operation

$8-3=5$

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Step1: Distribute the 5 to terms inside

$7x+5(1-x)=7x+5-5x$

Step2: Combine like terms

$7x+5-5x=2x+5$

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Step1: Multiply the two negative terms

$(-2)(-y)=2y$

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Step1: Subtract 5 from both sides

$5+2n-5=12-5 \implies 2n=7$

Step2: Divide by 2 on both sides

$n=\frac{7}{2}$

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Step1: Subtract $3y$ from both sides

$4y-7-3y=3y-4-3y \implies y-7=-4$

Step2: Add 7 to both sides

$y-7+7=-4+7 \implies y=3$

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Step1: Subtract $x$ from both sides

$6x-7-x=x+8-x \implies 5x-7=8$

Step2: Add 7 to both sides

$5x-7+7=8+7 \implies 5x=15$

Step3: Divide by 5 on both sides

$x=3$

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Step1: Multiply both sides by 2

$\frac{x}{2} \times 2=14 \times 2 \implies x=28$

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Step1: Combine like terms

$14x+3x-40=11 \implies 17x-40=11$

Step2: Add 40 to both sides

$17x-40+40=11+40 \implies 17x=51$

Step3: Divide by 17 on both sides

$x=3$

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Step1: Solve absolute value equation

$|x|=6 \implies x=6 \text{ or } x=-6$

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Step1: Translate to algebraic expression

Ten less than $x$ is $x-10$

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Step1: Convert mixed numbers to decimals

$2\frac{2}{3}\approx2.67$, $-2\frac{2}{5}=-2.4$

Step2: Order from least to greatest

$-4.33 < -3.68 < -2.4 < 1.22 < 2.67 < 4.12$

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Step1: Identify quadrant for $(-4,-8)$

Points with $x<0$ and $y<0$ are in Quadrant III

Answer:

1. $5$
2. $2x+5$
3. $2y$
4. $n=\frac{7}{2}$
5. $y=3$
6. $x=3$
7. $x=28$
8. $x=3$
9. $x=6$ or $x=-6$
10. $x-10$
11. $-4.33, -3.68, -2\frac{2}{5}, 1.22, 2\frac{2}{3}, 4.12$
12. Quadrant III