Which equation is equivalent to 4(p + 8) = 2(r – 6) when solved for r?

Answer:

[tex]r=2p+22[/tex]

Step-by-step explanation:

[tex]4(p+8)=2(r-6)\\4p+32=2r-12\\4p+32+12=2r\\4p+44=2r\\\frac{4p+44}{2} =\frac{2r}{2} \\2p+22=r[/tex]

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The equation equivalent to 4(p + 8) = 2(r – 6) when solved for r is

r = 2p + 22.

To solve for r in the equation 4(p + 8) = 2(r – 6), follow these steps:

1. Distribute the numbers: Distribute the numbers on both sides of the equation.

  [tex]\[4 \cdot p + 4 \cdot 8 = 2 \cdot r - 2 \cdot 6\][/tex]

2. Simplify: Perform the calculations on each side of the equation.

 [tex]\[4p + 32 = 2r - 12\][/tex]

3. Isolate r terms: Move the terms containing r to one side of the equation by adding 12 to both sides.

 [tex]\[4p + 32 + 12 = 2r\][/tex]

 [tex]\[4p + 44 = 2r\][/tex]

4. Divide by 2: Divide both sides by 2 to solve for r.

  [tex]\[\frac{4p + 44}{2} = r\][/tex]  

[tex]\[2p + 22 = r\][/tex]

Thus, the equation 4(p + 8) = 2(r – 6) when solved for r becomes r = 2p + 22.

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