Equation Combat Review Worksheet
DCA Unit 1 Practice
Equation Combat Review
Isolating variables, distributive property, and multi-step linear systems.
NAME:
DATE: PERIOD:
Directions: Solve each problem completely. For multiple-choice questions, select the best possible equivalent equation or solution. For open-response questions, write your step-by-step math in the space provided and enter your final answer in the designated box.
QUESTION 1
Which equation is equivalent to \(3x - 4y = 24\) when solved for \(y\)?
A
\(y = -\frac{4}{3}x - 8\)
B
\(y = -\frac{3}{4}x + 6\)
C
\(y = \frac{4}{3}x + 8\)
D
\(y = \frac{3}{4}x - 6\)
QUESTION 2
Determine the value of \(x\) that makes the equation true.
\(3 - 4x = -x - 9\)
Show Your Step-by-Step Work Here:
x =
Unit 1: Equations & Inequalities Page 1 of 4
Equation Combat Practice Review Algebra 1
QUESTION 3
What value of \(x\) makes the equation true?
\(-6x + 9 = 3(x - 12)\)
Show Work:
A
-3.5
B
3.5
C
-5
D
5
QUESTION 4
What value of \(p\) makes the equation true?
\(10 - 4(p + 3) = 15 - 2(2p + 5)\)
Show Work:
A
2
B
4
C
6
D
No solution
Unit 1: Equations & Inequalities Page 2 of 4
Equation Combat Practice Review Algebra 1
QUESTION 5
Evaluate \(p\) in the equation below.
\(3p - 2q = 12\)
A
\(p = \frac{2}{3}q - 4\)
B
\(p = 4 + \frac{2}{3}q\)
C
\(p = 4 - \frac{2}{3}q\)
D
\(p = 3 - \frac{3}{2}q\)
QUESTION 6
Solve the equation shown. Enter your answer in the box.
\(0.6(5x - 2) = -1.4x + 7.6\)
Show Work:
x =
QUESTION 7
Which of these below correctly solves for \(y\) of the equation \(2x - 3 = 5y + 4\)?
A
\(y = 2x + 4\)
B
\(y = -\frac{2}{5}x + \frac{7}{5}\)
C
\(y = -2x - 4\)
D
\(y = \frac{2}{5}x - \frac{7}{5}\)
Unit 1: Equations & Inequalities Page 3 of 4
Equation Combat Practice Review Algebra 1
QUESTION 8
The equation below can be used to determine \(V\), the volume of a rectangular prism.
\(V = lwh\)
where \(l\) is the length, \(w\) is the width, and \(h\) is the height of the prism. Which of these is the equation solved in terms of \(w\)?
A
\(w = \frac{lh}{V}\)
B
\(w = \frac{V}{lh}\)
C
\(w = \frac{Vh}{l}\)
D
\(w = \frac{Vl}{h}\)
QUESTION 9
A triangle has a height of \((2n - 4)\) inches and a base of 10 inches. A rectangle has a length of 6 inches and a width of \((2 + n)\) inches. The area in square inches of the triangle is equal to the area in square inches of the rectangle. What is the value of \(n\)?
Show Work:
n =
QUESTION 10
Rewrite the equation \(y - 6 = 3(x + 4)\) in slope-intercept form. Enter your answer in the box.
Show Work:
y =
Unit 1: Equations & Inequalities Page 4 of 4
Equation Combat Answer Key
ANSWER KEY
Teacher Reference
Equation Combat Answer Key
Detailed solutions and marking schemes for all 10 questions.
NAME: TEACHER COPY
DATE: ANSWER KEY PERIOD: ALL
QUESTION 1 KEY
Which equation is equivalent to \(3x - 4y = 24\) when solved for \(y\)?
A
\(y = -\frac{4}{3}x - 8\)
B
\(y = -\frac{3}{4}x + 6\)
C
\(y = \frac{4}{3}x + 8\)
D
\(y = \frac{3}{4}x - 6\) (Correct)
Explanation:
\(3x - 4y = 24 \implies -4y = -3x + 24 \implies y = \frac{-3}{-4}x + \frac{24}{-4} \implies y = \frac{3}{4}x - 6\)
QUESTION 2 KEY
Determine the value of \(x\) that makes the equation true.
\(3 - 4x = -x - 9\)
Teacher Solutions Steps:
1. Add \(4x\) to both sides: \(3 = 3x - 9\)
2. Add \(9\) to both sides: \(12 = 3x\)
3. Divide both sides by \(3\): \(x = 4\)
Verification: \(3 - 4(4) = 3 - 16 = -13\); \(-(4) - 9 = -13\). Correct!
x =
4
Unit 1: Equations & Inequalities (Answer Key) Page 1 of 4
Equation Combat Answer Key Algebra 1
QUESTION 3 KEY
What value of \(x\) makes the equation true?
\(-6x + 9 = 3(x - 12)\)
Solution Steps:
\(-6x + 9 = 3x - 36\) (distribute \(3\))
\(9 = 9x - 36\) (add \(6x\) to both sides)
\(45 = 9x \implies x = 5\) (add \(36\) then divide by \(9\))
A
-3.5
B
3.5
C
-5
D
5 (Correct)
QUESTION 4 KEY
What value of \(p\) makes the equation true?
\(10 - 4(p + 3) = 15 - 2(2p + 5)\)
Solution Steps:
\(10 - 4p - 12 = 15 - 4p - 10\) (distribute)
\(-4p - 2 = -4p + 5\) (combine like terms)
\(-2 = 5\) (add \(4p\) to both sides - untrue statement) \(\implies\) No solution
A
2
B
4
C
6
D
No solution (Correct)
Unit 1: Equations & Inequalities (Answer Key) Page 2 of 4
Equation Combat Answer Key Algebra 1
QUESTION 5 KEY
Evaluate \(p\) in the equation below.
\(3p - 2q = 12\)
A
Equation Combat Warm-up Handout
Daily Focus
Equation Combat Warm-up
Ready your mind for battle with these two quick warmup challenges.
NAME:
DATE: PERIOD:
Directions: Solve the following two problems independently. Show every mathematical step clearly so you can trace your logic.
CHALLENGE 1: MULTI-STEP SOLVING
Solve the equation below to determine the value of \(x\) that makes the relationship true.
\(2(x - 4) = -3x + 7\)
Show Your Step-by-Step Work:
x =
CHALLENGE 2: LITERAL EQUATION ISOLATION
Solve the equation below to isolate the variable \(a\).
\(5a - 2b = 10\)
Show Your Step-by-Step Work:
a =
Unit 1: Equations & Inequalities (Daily Warm-up) Warm-up Handout
