The property of equality that justifies the step from \( 3z/2 - 5 = 10 \) to \( 3z/2 - 5 + 5 = 10 + 5 \) is the Addition Property of Equality. This property states that if you add the same number to both sides of an equation, the two sides remain equal. In this case, both sides of the equation have 5 added to them.
Which property of equality justifies the step for solving the equation that is displayed?
3z/2−5=10
3z/2−5+5=10+5
3z/2=15
(1 point)
5 answers
how to
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Which property of equality justifies the step for solving the equation that is displayed?
3z/2−5=10
3z/2−5+5=10+5
3z/2=15
(1 point)
how to
3z/2−5=10
3z/2−5+5=10+5
3z/2=15
(1 point)
how to
To justify the step in the equation you've provided, follow these instructions:
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Identify the original equation: You start with: \[ \frac{3z}{2} - 5 = 10 \]
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Identify the operation you want to perform: To isolate \(\frac{3z}{2}\), you need to eliminate the \(-5\) on the left side. This is achieved by adding 5 to both sides of the equation.
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Apply the Addition Property of Equality: The Addition Property of Equality states that if you add the same value to both sides of an equation, the equation remains balanced (equal). In your case, adding 5 to both sides: \[ \frac{3z}{2} - 5 + 5 = 10 + 5 \]
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Simplify both sides: After adding 5, the left side simplifies to \(\frac{3z}{2}\): \[ \frac{3z}{2} = 15 \]
So, the property that justifies the step from \(\frac{3z}{2} - 5 = 10\) to \(\frac{3z}{2} = 15\) is the Addition Property of Equality because you are adding the same number (5) to both sides of the equation.
Quick Summary:
- Property Used: Addition Property of Equality
- Process: You added 5 to both sides of the equation to isolate \(\frac{3z}{2}\).