HOW DO YOU DO THIS? PLEASE SHOW WORK ASAP!
2 answers:
In general, you can do all of them this way.
1. Eliminate parentheses using the distributive property.
2. Collect terms.
3. Identify the variable term with the smallest (most negative) coefficient.
4. Add the opposite of everything on that side of the inequality and simplify.
5. Divide by the coefficient of the variable.
6. Add the opposite of the constant.
Using problem #5 as an example:
7x -3(4x -8) ≤ 6x +12 -9x
7x -12x +24 ≤ 6x +12 -9x . . . . . eliminate parentheses
-5x +24 ≤ -3x +12 . . . . . . . . . . . collect terms. Left side has smallest x term.
0 ≤ 5x -3x -24 +12 . . . . . . . . . . add opposite of left side
0 ≤ 2x -12 . . . . . . . . . . . . . . . . . collect terms
0 ≤ x -6 . . . . . . . . . . . . . . . . . . . divide by x-coefficient, 2
6 ≤ x . . . . . . . . . . . . . . . . . . . . . add the opposite of -6
Other answers are ...
2. m < -3/2 . . . . . . . . . . . . graphed as an open circle at -3/2 and a line to the left
3. x ≤ 11 . . . . . . . . . . . . . . . graphed as solid circle at 11 and line to the left
4. -1 ≤ x . . . . . . . . . . . . . . . graphed as solid circle at -1 and line to the right
1. Eliminate parentheses using the distributive property.
2. Collect terms.
3. Identify the variable term with the smallest (most negative) coefficient.
4. Add the opposite of everything on that side of the inequality and simplify.
5. Divide by the coefficient of the variable.
6. Add the opposite of the constant.
Using problem #5 as an example:
7x -3(4x -8) ≤ 6x +12 -9x
7x -12x +24 ≤ 6x +12 -9x . . . . . eliminate parentheses
-5x +24 ≤ -3x +12 . . . . . . . . . . . collect terms. Left side has smallest x term.
0 ≤ 5x -3x -24 +12 . . . . . . . . . . add opposite of left side
0 ≤ 2x -12 . . . . . . . . . . . . . . . . . collect terms
0 ≤ x -6 . . . . . . . . . . . . . . . . . . . divide by x-coefficient, 2
6 ≤ x . . . . . . . . . . . . . . . . . . . . . add the opposite of -6
Other answers are ...
2. m < -3/2 . . . . . . . . . . . . graphed as an open circle at -3/2 and a line to the left
3. x ≤ 11 . . . . . . . . . . . . . . . graphed as solid circle at 11 and line to the left
4. -1 ≤ x . . . . . . . . . . . . . . . graphed as solid circle at -1 and line to the right
You might be interested in