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Consider the following equations and name the property of equality used to solve for the variable.

A. x + 3.75 = 7

B. –3b = 18

C. m/5=-25

D. m – 4 = 9

Respuesta :

gmany

Step-by-step explanation:

[tex]A.\ x+3.75=7\qquad\text{subtract 3.75 from both sides}\\\\\boxed{\text{the subtraction property of equality}}\\\\x=3.25\\\\B.\ -3b=18\qquad\text{divide both sides by (-3)}\\\\\boxed{\text{the division property of equality}}\\\\b=-6\\\\C.\ \dfrac{m}{5}=-25\qquad\text{multiply both sides by 5}\\\\\boxed{\text{the multiplication property of equality}}\\\\m=-125\\\\D.\ m-4=9\qquad\text{add 4 to both sides}\\\\\boxed{\text{the addition property of equality}}\\\\m=13[/tex]

The property of equality used to solve for the variables are the Division, Subtraction, Multiplication and Addition properties

We will consider each of the questions one after the other

  • For A. x + 3.75 = 7

To solve for the variable in the equation, we will subtract 3.75 from both sides, that is

[tex]x + 3.75 - 3.75 = 7 - 3.75[/tex]

[tex]x = 3.25[/tex]

The property of equality used to solve for the variable is the Subtraction property

  • For B. –3b = 18

To solve for the variable in the equation, we will divide both sides by –3, that is,

[tex]\frac{-3b}{-3} = \frac{18}{-3}[/tex]

∴ [tex]b = -6[/tex]

The property of equality used to solve for the variable is the Division property

  • For C. m/5=-25

This can be written as

[tex]\frac{m}{5} = -25[/tex]

To solve for the variable, we will multiply both sides by 5

[tex]5 \times \frac{m}{5} = -25 \times 5[/tex]

∴ [tex]m = -75[/tex]

The property of equality used to solve for the variable is the Multiplication property

  • For D. m – 4 = 9

To solve for the variable, we will add 4 to both sides, that is

[tex]m - 4 +4 = 9 + 4[/tex]

∴ [tex]m = 13[/tex]

The property of equality used to solve for the variable is the Addition property

Hence, the property of equality used to solve for the variables are the Division, Subtraction, Multiplication and Addition properties

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