Solve for x 5/4(x-5/2)=-5/8

Solution:

Step 1:

Multiply both sides of the equation by $\frac{4}{5}$ to eliminate the fraction on the left side.

$$\frac{4}{5} \times \frac{5}{4}(x - \frac{5}{2}) = \frac{4}{5} \times (-\frac{5}{8})$$

Step 2:

Simplify the equation.

Step 2.1:

Start with simplifying the left side of the equation.

Step 2.1.1:

Use the distributive property to open the brackets.

$$\frac{4}{5} \times (\frac{5}{4}x - \frac{5}{4} \times \frac{5}{2}) = \frac{4}{5} \times (-\frac{5}{8})$$

Step 2.1.2:

Simplify the terms inside the brackets by multiplying.

$$\frac{4}{5} \times (\frac{5x}{4} - \frac{25}{8}) = \frac{4}{5} \times (-\frac{5}{8})$$

Step 2.1.3:

Apply the distributive property again to eliminate the brackets.

$$x - \frac{4}{5} \times \frac{25}{8} = \frac{4}{5} \times (-\frac{5}{8})$$

Step 2.2:

Now, simplify the right side of the equation.

Step 2.2.1:

Multiply the fraction by $\frac{4}{5}$.

$$x - \frac{4}{5} \times \frac{25}{8} = -\frac{4}{5} \times \frac{5}{8}$$

Step 2.2.2:

Simplify the multiplication.

$$x - \frac{4 \times 25}{5 \times 8} = -\frac{4 \times 5}{5 \times 8}$$

Step 2.2.3:

Reduce the fractions by canceling out common factors.

$$x - \frac{1 \times 25}{1 \times 2} = -\frac{1 \times 1}{1 \times 2}$$

Step 2.2.4:

Complete the simplification.

$$x - \frac{25}{2} = -\frac{1}{2}$$

Step 3:

Isolate the variable $x$ by moving all other terms to the opposite side.

Step 3.1:

Add $\frac{25}{2}$ to both sides of the equation to move the constant term to the right side.

$$x = -\frac{1}{2} + \frac{25}{2}$$

Step 3.2:

Combine like terms on the right side.

$$x = \frac{24}{2}$$

Step 3.3:

Simplify the fraction on the right side to find the value of $x$.

$$x = 12$$

Knowledge Notes:

To solve the equation $\frac{5}{4}(x - \frac{5}{2}) = -\frac{5}{8}$, we follow these steps:

1. Multiplication by the reciprocal: To eliminate the fraction on one side of the equation, we can multiply both sides by the reciprocal of the fraction's coefficient.

2. Distributive property: This property allows us to multiply a single term and two or more terms inside a set of parentheses. It's given by $a(b + c) = ab + ac$.

3. Combining like terms: This involves adding or subtracting terms that have the same variable raised to the same power.

4. Simplifying fractions: To simplify a fraction, we look for common factors in the numerator and the denominator and divide them out.

5. Isolating the variable: We want to get the variable on one side of the equation and all other terms on the opposite side. This often involves adding or subtracting terms on both sides of the equation.

6. Solving simple equations: Once we have isolated the variable, we can solve the equation by performing any remaining arithmetic operations.