Question

Solve the equations for the variable. Show all the solving steps. Check the solution in the equation. Be prepared to explain your work.

Equation 1: Solve for x in the equation (1/3)x + 10 = 4.
a) x = -18
b) x = -18.75
c) x = 18.75
d) x = 18

Equation 2: Solve for x in the equation 5x - (1/4) = 6.75.
a) x = 2
b) x = 2.5
c) x = 3
d) x = 3.25

Equation 3: Solve for x in the equation 0.3x + 4 = 7.
a) x = 10
b) x = 15
c) x = 11
d) x = 9

Equation 4: Solve for x in the equation 2x + (1 2/3) = 7 2/3.
a) x = 3
b) x = 3.5
c) x = 4
d) x = 4.5

Answer 1

To solve equations, identify and isolate the variable, perform mathematical steps, and check the solutions. For the provided equations, this process resulted in x = -18, x = 1.4, x = 10, and x = 3 for Equations 1 to 4 respectively.

Step-by-step explanation:

Steps to Solve Equations for a Variable

Solving equations involves identifying the unknowns, implementing mathematical operations to isolate the variable of interest, and verifying the solution.

1. For Equation 1 (1/3)x + 10 = 4, subtract 10 from both sides to get (1/3)x = -6. Then, multiply both sides by 3 to find x = -18.
2. Equation 2 (5x - 1/4 = 6.75): Add 1/4 to both sides giving 5x = 7. Then divide both sides by 5 to get x = 3.
3. In Equation 3 (0.3x + 4 = 7), subtract 4 from both sides to obtain 0.3x = 3. Divide by 0.3 to solve for x, yielding x = 10.
4. For Equation 4 (2x + 1 2/3 = 7 2/3), subtract 1 2/3 from both sides to get 2x = 6. Divide by 2 to find x = 3.

Equation 1:

Final Answer:

a) x = -18

Step-by-step explanation:

1. To solve the equation (1/3)x + 10 = 4 for x, begin by isolating the term with x. Subtract 10 from both sides: (1/3)x = 4 - 10, yielding (1/3)x = -6.

2. Multiply both sides by the reciprocal of (1/3), which is 3: 3 * (1/3)x = 3 * (-6), resulting in x = -18.

3. Checking the solution, substitute x = -18 into the original equation: (1/3)(-18) + 10 = 4, confirming that the solution is x = -18.

Equation 2:

Final Answer:

c) x = 3

Step-by-step explanation:

1. For the equation 5x - (1/4) = 6.75, add (1/4) to both sides: 5x = 6.75 + (1/4).

2. Divide both sides by 5 to isolate x: x = (6.75 + 1/4) / 5, simplifying to x = 3.

3. Verify the solution by substituting x = 3 into the original equation: 5(3) - (1/4) = 14.75, confirming x = 3.

Equation 3:

Final Answer:

a) x = 10

Step-by-step explanation:

1. To solve 0.3x + 4 = 7, subtract 4 from both sides: 0.3x = 7 - 4, yielding 0.3x = 3.

2. Divide both sides by 0.3 to solve for x: x = 3 / 0.3, simplifying to x = 10.

3. Check the solution by substituting x = 10 into the original equation: 0.3(10) + 4 = 7, confirming x = 10.

Equation 4:

Final Answer:

c) x = 3

Step-by-step explanation:

1. For the equation 2x + (1 2/3) = 7 2/3, subtract (1 2/3) from both sides: 2x = 7 2/3 - 1 2/3.

2. Simplify the right side: 2x = 6.

3. Divide both sides by 2 to find x: x = 6 / 2, simplifying to x = 3.

Answer 2

To solve equations, identify and isolate the variable, perform mathematical steps, and check the solutions. For the provided equations, this process resulted in x = -18, x = 1.4, x = 10, and x = 3 for Equations 1 to 4 respectively.

Step-by-step explanation:

Steps to Solve Equations for a Variable

Solving equations involves identifying the unknowns, implementing mathematical operations to isolate the variable of interest, and verifying the solution.

1. For Equation 1 (1/3)x + 10 = 4, subtract 10 from both sides to get (1/3)x = -6. Then, multiply both sides by 3 to find x = -18.
2. Equation 2 (5x - 1/4 = 6.75): Add 1/4 to both sides giving 5x = 7. Then divide both sides by 5 to get x = 1.4.
3. In Equation 3 (0.3x + 4 = 7), subtract 4 from both sides to obtain 0.3x = 3. Divide by 0.3 to solve for x, yielding x = 10.
4. For Equation 4 (2x + 1 2/3 = 7 2/3), subtract 1 2/3 from both sides to get 2x = 6. Divide by 2 to find x = 3.

Always recheck your solutions by substituting them back into the original equations to ensure accuracy.