The real x for which 2(2x + 3) - 10 < 6 (x - 2) is :
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Step-by-Step Solution
Step 1: Expand both sides of the inequality
First, we distribute the numbers outside the parentheses to the terms inside on both sides of the inequality. On the left side, 2×2x=4x and 2×3=6. On the right side, 6×x=6x and 6×−2=−12.
Step 2: Simplify both sides
Next, we combine the constant terms on the left side of the inequality. 6−10 simplifies to −4. The right side remains 6x−12.
Step 3: Collect x terms on one side
To isolate the variable x, we move all terms containing x to one side and constant terms to the other. Subtract 6x from both sides and add 4 to both sides.
Step 4: Simplify and solve for x
Combine the terms: 4x−6x=−2x and −12+4=−8. Finally, divide both sides by −2. Remember to reverse the inequality sign when dividing by a negative number.