Drag each step and justification to the correct location on the table. Each step and justification can be used more than once, but not all steps and justifications will be used.
Order each step and justification that is needed to solve the equation below.
[tex]\frac{2}{3} y+15=9[/tex]
[tex]\frac{2}{3} y=-6 \quad y=9 \quad[/tex] Multiplication property of equality [tex]\quad \frac{2}{3} y \cdot \frac{3}{2}=6 \cdot \frac{3}{2}[/tex]
[tex]\frac{2}{3} y \cdot \frac{3}{2}=-6 \cdot \frac{3}{2} \quad \frac{2}{3} y=6 \quad[/tex] Subtraction property of equality [tex]\quad y=-9[/tex]
Steps
Justifications
[tex]\frac{2}{3} y+15=9[/tex]
Given
[tex]\frac{2}{3} y+15-15=9-15[/tex]
Simplification
Simplification
Answer (2)
Subtract 15 from both sides: 3 2 y + 15 − 15 = 9 − 15 .
Simplify: 3 2 y = − 6 .
Multiply both sides by 2 3 : 3 2 y ⋅ 2 3 = − 6 ⋅ 2 3 .
Simplify to find the solution: y = − 9 .
Explanation
Problem Analysis We are given the equation 3 2 y + 15 = 9 and we want to solve for y . We will perform operations on both sides of the equation to isolate y .
Subtracting 15 from both sides First, we subtract 15 from both sides of the equation to isolate the term with y : 3 2 y + 15 − 15 = 9 − 15
Simplification Simplifying both sides, we get: 3 2 y = − 6
Multiplying by the reciprocal Next, we multiply both sides of the equation by 2 3 to isolate y : 3 2 y ⋅ 2 3 = − 6 ⋅ 2 3
Simplification Simplifying both sides, we get: y = − 9
Final Answer Therefore, the solution to the equation is y = − 9 .
Examples
Imagine you're baking a cake and need to adjust the recipe. If 3 2 of a cup of sugar plus 15 grams is too sweet and you want it to be 9 grams, this equation helps you find the correct amount of sugar to use. Solving linear equations is crucial in many real-life scenarios, from cooking to managing finances. Understanding how to isolate variables allows you to adapt and solve problems efficiently.
To solve the equation 3 2 y + 15 = 9 , we isolate y by subtracting 15 from both sides to get 3 2 y = − 6 and then multiply both sides by 2 3 to find y = − 9 . The steps demonstrate the properties of equality used in algebra. The final answer is y = − 9 .
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