Question

Solve the following equations by applying the fundamental principle of equality. Remember to check your solution. a. \(35+x=167\) b. \(14 v=700\) c. \(w-27=101\) d. \(1350=15 y\) e. \(s+66=91\) f. \(33=p-11\) g. \(325 g=650\) h. \(0=d-42\) i. \(15 r=555\) j. \(3721=1295+x\) k, \(477=9 y\) l. \(826=z-284\) m. \(16 w=192\) n. \(x+439=1204\) o. \(32,065=5 t\)

Short answer

#tag_title#2. Verify the equality holds#tag_content#Confirm that the equation holds true: \(128-27 = 101\) In conclusion, the solutions for the given equations are: x = 132, v = 50, and w = 128.

Step-by-step solution

1. Isolate the variable

Subtract 35 from both sides of the equation to isolate x: \(x = 167 - 35\)

2. Evaluate the expression

Calculate the value of x: \(x = 132\) #a - Checking the solution#

1. Substitute the value of x into the original equation

Replace x with 132 in the equation: \(35+132=167\)

2. Verify the equality holds

Confirm that the equation holds true: \(35+132 = 167\) #b - Solving the equation 14 v=700#

1. Isolate the variable

Divide both sides of the equation by 14 to isolate v: \(v = \frac{700}{14}\)

2. Evaluate the expression

Calculate the value of v: \(v = 50\) #b - Checking the solution#

1. Substitute the value of v into the original equation

Replace v with 50 in the equation: \(14\cdot 50=700\)

2. Verify the equality holds

Confirm that the equation holds true: \(14\cdot 50 = 700\) #c - Solving the equation w-27=101#

1. Isolate the variable

Add 27 to both sides of the equation to isolate w: \(w = 101 + 27\)

2. Evaluate the expression

Calculate the value of w: \(w = 128\) #c - Checking the solution#

1. Substitute the value of w into the original equation

Replace w with 128 in the equation: \(128-27=101\)