Solve equations of the form |ax + b| = c step-by-step.
|ax + b| = c
This calculator helps you solve absolute value equations of the form |ax + b| = c quickly and accurately. Enter the coefficient, constant, and absolute value, and it computes both solutions automatically while showing clear error messages if no solution exists.
Provide the values for:
The calculator uses these inputs to find both possible solutions for x.
The calculator ensures valid inputs:
This ensures accurate and meaningful results every time.
Learn how absolute value equations are solved:
This helps beginners understand the logic behind absolute value equations.
The results are updated in real-time as you type:
Using this calculator is simple and intuitive. Here's what happens behind the scenes:
This allows you to explore different numbers quickly, check your homework, and understand how absolute value equations behave in algebra—all without showing complicated formulas.
Absolute value equations are equations where the variable is inside an absolute value symbol, such as |ax + b| = c. The absolute value represents the distance of a number from zero on the number line, so it is always non-negative. To solve these equations, we consider both possible cases for the value inside the absolute value.
|ax + b| = c → ax + b = c or ax + b = -c
This means that for any equation in the form |ax + b| = c:
Solving for x in both cases, the formula becomes:
x = (c - b) / a or x = (-c - b) / a
In this formula:
Solve the equation:
|2x − 3| = 5
Step 1 – Split into two equations:
2x − 3 = 5
2x − 3 = −5
Step 2 – Solve for x:
x = 4
x = −1
The calculator automatically shows both solutions instantly, making learning easy and visual.
Everything you need to know about solving equations of the form |ax + b| = c quickly and accurately.
This calculator solves absolute value equations of the form |ax + b| = c. It computes both possible solutions automatically and displays them clearly for easy understanding.
Yes! The calculator is completely free, with no registration, ads, or hidden charges.
You need to enter the coefficient of x (a), the constant term (b), and the absolute value (c). The calculator uses these to find both solutions.
Yes. The calculator handles positive, negative, and zero values for a and b. However, the absolute value c must be zero or positive; otherwise, the equation has no solution.
If a = 0 or c < 0, the calculator displays a clear error message, as no valid solution exists in these cases.
It applies the absolute value rule: |ax + b| = c leads to two cases: ax + b = c and ax + b = −c. Both equations are solved for x and displayed as the two possible solutions.
Yes. Use the “Clear All” button to reset the input fields, or the “Reload Calculator” button to reload the page completely.
Yes, the calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktops.
The results are rounded to two decimal places if necessary, providing precise and easy-to-read solutions for both possible values of x.
Students, teachers, or anyone learning algebra can use this tool to solve absolute value equations quickly, check homework, or understand the step-by-step solution process.
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