1.1(3x+5)is equal to or greater than 1.6-(x+3)
How do you solve this to make a fraction?
To solve the given inequality and express the solution as a fraction, you'll follow these steps:
Step 1: Simplify both sides of the inequality.
Step 2: Isolate the variable on one side of the inequality.
Step 3: Solve for the variable.
Step 4: Express the solution as a fraction, if possible.
Now let's go through the step-by-step solution:
Step 1: Simplify both sides of the inequality.
Multiply 1.1 by each term inside the parentheses:
1.1 * 3x = 3.3x
1.1 * 5 = 5.5
This gives us:
3.3x + 5.5 ≥ 1.6 - (x + 3)
Step 2: Isolate the variable on one side of the inequality.
Distribute the negative sign to the terms inside the parentheses:
3.3x + 5.5 ≥ 1.6 - x - 3
Combine like terms to simplify:
3.3x + 5.5 ≥ -x - 1.4
Step 3: Solve for the variable.
To solve for x, you need to move all the x terms to one side and the constant terms to the other side of the inequality. Let's do that by adding x and subtracting 5.5 from both sides:
3.3x + x ≥ -1.4 - 5.5
Combine like terms:
4.3x ≥ -6.9
Step 4: Express the solution as a fraction.
To express the solution as a fraction, divide both sides of the inequality by 4.3:
x ≥ -6.9/4.3 (the inequality sign remains the same)
Simplify the fraction, if possible:
x ≥ -1.605
Therefore, the solution to the given inequality expressed as a fraction is x ≥ -1.605.