The value of p that makes the equation true is -20
Step-by-step explanation:
To solve an equation of one variable
∵ The equation is [tex]\frac{3}{5}p+\frac{1}{5}(40 - p)=0[/tex]
- Simplify the left hand side
∵ [tex]\frac{1}{5}(40-p)=\frac{1}{5}(40)-\frac{1}{5}(p)[/tex]
∴ [tex]\frac{1}{5}(40-p)=8-\frac{1}{5}p[/tex]
- Substitute [tex]\frac{1}{5}(40-p)[/tex] in the equation by [tex]8-\frac{1}{5}p[/tex]
∴ [tex]\frac{3}{5}p+8-\frac{1}{5}p=0[/tex]
- Add the like terms
∴ [tex](\frac{3}{5}p-\frac{1}{5}p)+8=0[/tex]
∴ [tex]\frac{2}{5}p+8=0[/tex]
- Subtract 8 from both sides
∴ [tex]\frac{2}{5}p=-8[/tex]
- Divide both sides by [tex]\frac{2}{5}[/tex]
∴ p = -20
To check the answer substitute p by -20 in the equation, the left hand side is equal to the right hand side, then the answer is right
∵ left hand side = [tex]\frac{3}{5}(-20)+\frac{1}{5}(40-(-20))[/tex]
∴ left hand side = [tex]\frac{-60}{5}+\frac{1}{5}(40+20)[/tex]
∴ left hand side = [tex]\frac{-60}{5}+\frac{60}{5}[/tex]
∴ left hand side = 0
∵ Right hand side = 0
∴ Left hand side = Right hand side
∴ The value of p makes the equation true
The value of p that makes the equation true is -20
Learn more:
You can learn more about the equations in brainly.com/question/11229113
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