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[/tex] Subtraction property of equality [tex]\quad \frac{2}{3} y \cdot \frac{3}{2}=-6 \cdot \frac{3}{2} \quad \frac{2}{3} y=-6[/tex]
Multiplication property of equality [tex]\quad \frac{2}{3} y \cdot \frac{3}{2}=6 \cdot \frac{3}{2} \quad y=9 \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 value of y : y = − 9 .
Explanation
Problem Analysis We are given the equation 3 2 y + 15 = 9 and we need to solve for y . We will use algebraic manipulations to isolate y on one side of the equation.
Subtracting 15 from both sides First, we subtract 15 from both sides of the equation using the subtraction property of equality: 3 2 y + 15 − 15 = 9 − 15
Simplification Next, we simplify both sides of the equation: 3 2 y = − 6
Multiplying by the reciprocal Now, we multiply both sides of the equation by 2 3 using the multiplication property of equality: 3 2 y ⋅ 2 3 = − 6 ⋅ 2 3
Simplification Finally, we simplify both sides to find the value of y : y = − 9
Examples
Solving linear equations is a fundamental skill in algebra and is used in various real-life situations. For example, if you want to determine how many hours you need to work to earn a certain amount of money, you can set up a linear equation and solve for the number of hours. Similarly, if you are calculating the cost of a project and have some fixed costs and some variable costs, you can use a linear equation to model the total cost and solve for the unknown variables.
To solve the equation 3 2 y + 15 = 9 , we subtract 15 from both sides to get 3 2 y = − 6 . We then multiply both sides by 2 3 to isolate y , leading to y = − 9 .
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