Problem 96 Solve each equation. $$ 4 x-... [FREE SOLUTION]

Chapter 8: Problem 96

Solve each equation. $$ 4 x-7=0 $$

Short Answer

Expert verified

x = \frac{7}{4}

Step by step solution

- Add 7 to both sides

To isolate the term with the variable, add 7 to both sides of the equation: \[ 4x - 7 + 7 = 0 + 7 \] This simplifies to: \[ 4x = 7 \]

- Divide both sides by 4

Now, to solve for $ x $, divide both sides of the equation by 4: \[ \frac{4x}{4} = \frac{7}{4} \] This simplifies to: \[ x = \frac{7}{4} \]

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

isolate the variable

When solving linear equations, the main goal is to isolate the variable (usually represented by a letter like x) on one side of the equation. This makes it easy to see the value of the variable clearly. In the given problem, we start with the equation:
4x - 7 = 0
To isolate the variable x, we need to get rid of any constants (numbers without the variable) and coefficients (numbers multiplying the variable) attached to x. By performing the same mathematical operations on both sides of the equation, we maintain the equality.

addition property of equality

The addition property of equality states that you can add the same number to both sides of an equation without changing the equation's solution. This is an essential principle when solving for a variable.
In our example, we need to eliminate the -7 on the left side of the equation. To do this, we add 7 to both sides:
4x - 7 + 7 = 0 + 7
This simplifies to:
4x = 7
Adding 7 removes the -7 from the left side, isolating the term with the variable (4x).

division property of equality

The division property of equality tells us that we can divide both sides of an equation by the same non-zero number without changing the solution. This property is especially useful for getting rid of coefficients attached to variables.
In our problem, we now have:
4x = 7
To isolate x, we need to divide both sides by 4:
$\frac{4x}{4} = \frac{7}{4}$
This simplifies to:
x = $\frac{7}{4}$
By dividing both sides by 4, we have isolated the variable x, and found that its value is $\frac{7}{4}$.

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91影视

Solve each equation. $$ 4 x-7=0 $$

Short Answer

Step by step solution

- Add 7 to both sides

- Divide both sides by 4

Key Concepts

isolate the variable

addition property of equality

division property of equality

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