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Mice21 [21]
3 years ago
8

Solve 48 = 5(2x - 7) + 3. Justify each step.

Mathematics
2 answers:
valina [46]3 years ago
8 0

Answer:

x=8

Step-by-step explanation:

48=5(2x-7)+3

Use the distributive property

48=10x-35+3

Combine like terms

48=10x-32

Add 32 to both sides to cancel out the negative 32

80=10x

x=8

Svetlanka [38]3 years ago
5 0

Answer:

x = 8

Step-by-step explanation:

Step 1: Write equation

48 = 5(2x - 7) + 3

Step 2: Solve for <em>x</em>

  1. Distribute 5: 48 = 10x - 35 + 3
  2. Combine like terms: 48 = 10x - 32
  3. Add 32 to both sides: 80 = 10x
  4. Divide both sides by 10: 8 = x
  5. Rewrite: x = 8

Step 3: Check

<em>Plug in x to verify it's a solution.</em>

48 = 5(2(8) - 7) + 3

48 = 5(16 - 7) + 3

48 = 5(9) + 3

48 = 45 + 3

48 = 48

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Step-by-step explanation:

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  • <em>there's</em><em> </em><em>a</em><em> </em><em>"</em><em>-21</em><em>"</em><em> </em><em>next</em><em> </em><em>to</em><em> </em><em>"</em><em>5n</em><em>"</em><em>,</em><em> </em><em>inverse</em><em> </em><em>of</em><em> </em><em>subtraction</em><em> </em><em>is</em><em> </em><em>addition</em><em>,</em><em> </em><em>so</em><em> </em><em>add</em><em> </em><em>21</em><em> </em><em>on</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>equation</em><em>.</em><em> </em>

=> m + 21 = 5n <u>-</u> <u>21</u> + <u>21</u>

=> m+ 21 = 5n

  • <em>There's</em><em> </em><em>also</em><em> </em><em>a</em><em> </em><em>5</em><em> </em><em>attached</em><em> </em><em>to</em><em> </em><em>n</em><em>,</em><em> </em><em>that</em><em> </em><em>means</em><em> </em><em>the</em><em> </em><em>multiplication</em><em> </em><em>of</em><em> </em><em>n</em><em> </em><em>with</em><em> </em><em>5</em><em>,</em><em> </em><em>the</em><em> </em><em>inverse</em><em> </em><em>of</em><em> </em><em>multiplication</em><em> </em><em>is</em><em> </em><em>division</em><em>,</em><em> </em><em>so</em><em> </em><em>dividing</em><em> </em><em>both</em><em> </em><em>sides</em><em> </em><em>of</em><em> </em><em>the</em><em> </em><em>equation</em><em> </em><em>by</em><em> </em><em>5</em>

<em>\mathsf{ \frac{m + 21}{5} = n }</em>

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