By following these steps and applying basic algebraic operations, we found that the number that satisfies the given equation is 40. This solution demonstrates the process of solving for an unknown variable in a linear equation involving fractions.
Solving the Equation: 3/4x - 19 = 11 (Plagiarism-Free)
We're given the equation:
3/4x - 19 = 11
Our goal is to isolate and solve for x, the unknown number. Here's how we can do it:
1. Add 19 to both sides:
To get x by itself, we need to isolate it. Adding 19 to both sides of the equation will remove the subtraction and keep the variable on one side:
3/4x = 19 + 11
2. Combine like terms:
Adding the constants on the right side simplifies the equation:
3/4x = 30
3. Multiply both sides by 4/3:
To isolate x completely, we need to get rid of the fraction. Multiplying both sides by the reciprocal of 3/4 (which is 4/3) will eliminate the fraction and leave x by itself:
x = 30 * (4/3)
4. Simplify:
Multiplying the numbers on the right side gives the final solution:
x = 40
Therefore, the number we're looking for is 40.
Explanation Breakdown:
We started by isolating x by adding 19 to both sides.
Then, we combined like terms to simplify the equation.
Finally, we multiplied both sides by the reciprocal of the fraction to isolate x and solve for its value.