Question

evaluate the following expressions using order of operations.
#1) $10 - 24 \div (5 - 3)^3$ #2) $4w + 5z - z^2$ given $w = -1$ and $z = 3$

#3) $12 - 8 + 16 \div (1 - 5) - 3^2$ #4) $a - b + 3c^2$ given $a = -1$, $b = 5$ and $c = -2$

simplify the following expressions by using distributive property and combining like terms.
#6) $10x + 2(3x - 1)$ #7) $7 - 2(x - 3)$
#8) $5x + 2x + 4(2x - 3)$

solve the following equations.
#9) $-3x + 1 = 19$ #10) $-3(2x - 4) + 10 = 5$ #11) $-2x + 5 = 9x - 1$

Explanation:

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For #1: $10 - 24 \div (5 - 3)^3$

Step1: Calculate parentheses

$5-3=2$

Step2: Calculate exponent

$2^3=8$

Step3: Perform division

$24\div8=3$

Step4: Perform subtraction

$10-3=7$

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For #2: $4w + 5z - z^2$; $w=-1,z=3$

Step1: Substitute values

$4(-1)+5(3)-3^2$

Step2: Calculate terms

$-4+15-9$

Step3: Compute final sum

$-4+15=11; 11-9=2$

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For #3: $12 - 8 + 16 \div (1 - 5) - 3^2$

Step1: Calculate parentheses

$1-5=-4$

Step2: Calculate exponent

$3^2=9$

Step3: Perform division

$16\div(-4)=-4$

Step4: Compute left to right

$12-8=4; 4+(-4)=0; 0-9=-9$

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For #4: $A - B + 3C^2$; $A=-1,B=5,C=-2$

Step1: Substitute values

$-1-5+3(-2)^2$

Step2: Calculate exponent

$(-2)^2=4$

Step3: Multiply then sum

$-1-5=-6; 3\times4=12; -6+12=6$

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For #6: $10x + 2(3x - 1)$

Step1: Apply distributive property

$10x+6x-2$

Step2: Combine like terms

$16x-2$

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For #7: $7 - 2(x - 3)$

Step1: Apply distributive property

$7-2x+6$

Step2: Combine constants

$13-2x$

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For #8: $5x + 2x + 4(2x - 3)$

Step1: Apply distributive property

$5x+2x+8x-12$

Step2: Combine like terms

$15x-12$

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For #9: $-3x + 1 = 19$

Step1: Subtract 1 from both sides

$-3x=19-1=18$

Step2: Divide by -3

$x=\frac{18}{-3}=-6$

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For #10: $-3(2x - 4) + 10 = 5$

Step1: Apply distributive property

$-6x+12+10=5$

Step2: Combine constants

$-6x+22=5$

Step3: Isolate x term

$-6x=5-22=-17$

Step4: Solve for x

$x=\frac{-17}{-6}=\frac{17}{6}$

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For #11: $-2x + 5 = 9x - 1$

Step1: Collect x terms left

$-2x-9x=-1-5$

Step2: Simplify both sides

$-11x=-6$

Step3: Solve for x

$x=\frac{-6}{-11}=\frac{6}{11}$

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Answer:

1. $7$
2. $2$
3. $-9$
4. $6$
5. $16x-2$
6. $13-2x$
7. $15x-12$
8. $x=-6$
9. $x=\frac{17}{6}$
10. $x=\frac{6}{11}$