50+ algebra worksheets for 10th Grade on Quizizz | Free & Printable - Free Printable

Here are the step-by-step solutions for the problems shown in your worksheet.

1. $3 + 2^3 - 8$
* First, solve the exponent: $2^3 = 2 \times 2 \times 2 = 8$.
* Now the equation is: $3 + 8 - 8$.
* Add and subtract from left to right: $3 + 8 = 11$, and $11 - 8 = 3$.
* Correct Option: D

2. $6x - 2 - 7x + 4 - x$
* Group the $x$ terms together: $6x - 7x - x$.
* $6x - 7x = -1x$
* $-1x - 1x = -2x$
* Group the numbers together: $-2 + 4$.
* $-2 + 4 = 2$
* Combine them: $-2x + 2$.
* Correct Option: A

3. $-3(x - 3) + 6(x + 1)$
* Distribute the $-3$ into the first parenthesis: $-3 \cdot x = -3x$ and $-3 \cdot -3 = +9$. Result: $-3x + 9$.
* Distribute the $6$ into the second parenthesis: $6 \cdot x = 6x$ and $6 \cdot 1 = 6$. Result: $6x + 6$.
* Combine everything: $-3x + 9 + 6x + 6$.
* Combine $x$ terms: $-3x + 6x = 3x$.
* Combine numbers: $9 + 6 = 15$.
* Final result: $3x + 15$.
* Correct Option: D

4. $4a + 8 = -20$
* Subtract 8 from both sides to isolate the term with $a$:
* $4a = -20 - 8$
* $4a = -28$
* Divide by 4 to solve for $a$:
* $a = -28 / 4$
* $a = -7$
* Correct Option: B

5. $-5x - 10 < -30$
* Add 10 to both sides:
* $-5x < -30 + 10$
* $-5x < -20$
* Divide by $-5$. Important: When you divide or multiply an inequality by a negative number, you must flip the inequality sign (from $<$ to $>$).
* $x > -20 / -5$
* $x > 4$
* Correct Option: A

6. $8(x - 1) = 4(x + 4) - 2x$
* Distribute on both sides:
* Left side: $8x - 8$
* Right side: $4x + 16 - 2x$
* Simplify the right side ($4x - 2x = 2x$):
* $8x - 8 = 2x + 16$
* Move variables to one side and numbers to the other. Subtract $2x$ from both sides:
* $6x - 8 = 16$
* Add 8 to both sides:
* $6x = 24$
* Divide by 6:
* $x = 4$
* Correct Option: B

7. What is 16% of 34?
* Convert percentage to a decimal: $16\% = 0.16$.
* Multiply by the number: $0.16 \times 34$.
* Calculation: $16 \times 34 = 544$. Since there are two decimal places in 0.16, move the decimal two spots to the left: $5.44$.
* *(Note: The options for this question are cut off in the image, but the calculated answer is 5.44).*

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Final Answer:
1. D
2. A
3. D
4. B
5. A
6. B
7. 5.44