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Solve two-step inequalities in the form ax + b < c with step-by-step solutions
Inequality: 2x + 3 < 11
Two-step inequalities follow the format ax + b < c and require two operations to solve: first subtract (or add) to eliminate the constant term, then divide (or multiply) to isolate the variable.
Two-step inequalities are typically written as ax + b [operator] c, where:
The two steps to solve these inequalities are:
One-step inequalities require only one operation to solve (e.g., 2x < 6), while two-step inequalities require two operations (e.g., 2x + 3 < 11) - first removing the constant, then isolating the variable.
Always follow the reverse order of operations (PEMDAS backwards). First add/subtract to eliminate the constant term, then multiply/divide to isolate the variable. This is the opposite order of how the expression was built.
You only flip the sign in the second step if the coefficient (a) is negative. When you divide both sides by a negative number, the inequality sign must be reversed.
Yes! If b is negative, the inequality looks like 2x - 3 < 7. In the first step, you would add 3 to both sides (the opposite of subtracting 3).
Pick a value from your solution set and substitute it back into the original inequality. If it makes a true statement, your solution is likely correct. Test a boundary value and a value outside your solution set too.
Treat it the same way! Divide by the fraction (or multiply by its reciprocal). If the fraction is negative (like -1/2), remember to flip the inequality sign.
Yes! Multiplying by the reciprocal is equivalent to dividing. For example, dividing by 2 is the same as multiplying by 1/2. Just remember: if you multiply by a negative, flip the sign!
It's called two-step because you need exactly two operations to isolate the variable: one operation to handle the constant term, and one operation to handle the coefficient.
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