2x + 3y is less than or equal to 6
solve b=6c for c
The length of a rectangle is fixed at 15cm. What widths will make the perimeter greater than 80 cm?
solve the compound inequality:
6>-5x + 5 or 10 is less than or equal to -5x+4
1. 2x + 3y <= 6. Solve for ?
3y<= -2x + 6,
y = -2x/3 + 2.
2. b = 6c.
c = b/6.
3. Given: L = 15 cm.
2L + 2W > 80,
30 + 2W > 80,
2W > 80 - 30,
2W > 50,
W > 25 cm
4. I'm assuming both binomials =
-5x + 5.
6 > - 5x + 5 >= 10,
Subtract 5:
6 - 5 > -x >= 10 - 5,
1 > - 5x >= 5,
Multiply all terms by -5 and reverse
inequality sign:
1/-5 < x <= 5/-5,
-1/5 < x <= -1.
1. Ans: y <= -2x/3 + 2.
To solve the inequality 2x + 3y ≤ 6, you can follow these steps:
1. Begin by isolating the variable terms on one side of the inequality by subtracting 2x from both sides: 3y ≤ -2x + 6.
2. Next, divide both sides of the inequality by 3 to solve for y: y ≤ (-2/3)x + 2/3.
To solve b = 6c for c:
1. Divide both sides of the equation by 6 to isolate c: c = b/6.
To find the widths that will make the perimeter of a rectangle greater than 80 cm, given a fixed length of 15 cm:
1. Let's assume the width of the rectangle is represented by w.
2. The formula for the perimeter of a rectangle is given by P = 2(length + width), which in this case becomes 80 < 2(15 + w).
3. Simplify the expression: 80 < 30 + 2w.
4. Subtract 30 from both sides: 50 < 2w.
5. Divide both sides of the inequality by 2: 25 < w.
6. The width should be greater than 25 cm for the perimeter to be greater than 80 cm.
To solve the compound inequality 6 > -5x + 5 or 10 ≤ -5x + 4:
1. Begin by solving the first inequality: 6 > -5x + 5.
a. Subtract 5 from both sides: 1 > -5x.
b. Divide by -5, remembering to reverse the inequality sign since we're dividing by a negative number: -1/5 < x.
2. Next, solve the second inequality: 10 ≤ -5x + 4.
a. Subtract 4 from both sides: 6 ≤ -5x.
b. Divide by -5, remembering to reverse the inequality sign: -6/5 ≥ x.
Therefore, the solution to the compound inequality is -1/5 < x ≤ -6/5.