To solve the inequality 10 + 6z ≤ -8, we need to isolate z.
Subtract 10 from both sides:
10 + 6z - 10 ≤ -8 - 10
6z ≤ -18
Divide both sides by 6 (since the coefficient of z is 6):
(6z)/6 ≤ (-18)/6
z ≤ -3
The solution to the inequality is z ≤ -3.
To graph the solution, we plot all values of z that are less than or equal to -3 on a number line. In other words, we shade the portion of the number line to the left of -3, and include -3 as well.
Here is a graph of the solution on a number line:
<-----------|=========(-∞)============(-3)=============>
Solve the inequality and graph the solution. 10+6z≤ – 8
11 answers
Solve the inequality and graph the solution. 2+7v>16
To solve the inequality 2 + 7v > 16, we need to isolate v.
Subtract 2 from both sides:
2 + 7v - 2 > 16 - 2
7v > 14
Divide both sides by 7 (since the coefficient of v is 7):
(7v)/7 > (14)/7
v > 2
The solution to the inequality is v > 2.
To graph the solution, we plot all values of v that are greater than 2 on a number line. In other words, we shade the portion of the number line to the right of 2, excluding 2 itself.
Here is a graph of the solution on a number line:
<===========|=========2=======(-∞)==================>
Subtract 2 from both sides:
2 + 7v - 2 > 16 - 2
7v > 14
Divide both sides by 7 (since the coefficient of v is 7):
(7v)/7 > (14)/7
v > 2
The solution to the inequality is v > 2.
To graph the solution, we plot all values of v that are greater than 2 on a number line. In other words, we shade the portion of the number line to the right of 2, excluding 2 itself.
Here is a graph of the solution on a number line:
<===========|=========2=======(-∞)==================>
Solve the inequality and graph the solution. 6a+17>11
To solve the inequality 6a + 17 > 11, we need to isolate a.
Subtract 17 from both sides:
6a + 17 - 17 > 11 - 17
6a > -6
Divide both sides by 6 (since the coefficient of a is 6):
(6a)/6 > (-6)/6
a > -1
The solution to the inequality is a > -1.
To graph the solution, we plot all values of a that are greater than -1 on a number line. In other words, we shade the portion of the number line to the right of -1, excluding -1 itself.
Here is a graph of the solution on a number line:
<===========|==========(-1)=========(-∞)==================>
Subtract 17 from both sides:
6a + 17 - 17 > 11 - 17
6a > -6
Divide both sides by 6 (since the coefficient of a is 6):
(6a)/6 > (-6)/6
a > -1
The solution to the inequality is a > -1.
To graph the solution, we plot all values of a that are greater than -1 on a number line. In other words, we shade the portion of the number line to the right of -1, excluding -1 itself.
Here is a graph of the solution on a number line:
<===========|==========(-1)=========(-∞)==================>
Solve the inequality and graph the solution. – 2q–1≤7
To solve the inequality -2q - 1 ≤ 7, we need to isolate q.
Add 1 to both sides:
-2q - 1 + 1 ≤ 7 + 1
-2q ≤ 8
Divide both sides by -2 (since the coefficient of q is -2). Remember that when dividing an inequality by a negative number, we need to reverse the inequality symbol.
(-2q)/-2 ≥ (8)/-2
q ≥ -4
The solution to the inequality is q ≥ -4.
To graph the solution, we plot all values of q that are greater than or equal to -4 on a number line. In other words, we shade the portion of the number line to the right or equal to -4.
Here is a graph of the solution on a number line:
<=============[=======================(-4)=======================
Add 1 to both sides:
-2q - 1 + 1 ≤ 7 + 1
-2q ≤ 8
Divide both sides by -2 (since the coefficient of q is -2). Remember that when dividing an inequality by a negative number, we need to reverse the inequality symbol.
(-2q)/-2 ≥ (8)/-2
q ≥ -4
The solution to the inequality is q ≥ -4.
To graph the solution, we plot all values of q that are greater than or equal to -4 on a number line. In other words, we shade the portion of the number line to the right or equal to -4.
Here is a graph of the solution on a number line:
<=============[=======================(-4)=======================
Solve the inequality and graph the solution. 17+6c≤5
To solve the inequality 17 + 6c ≤ 5, we need to isolate c.
Subtract 17 from both sides:
17 + 6c - 17 ≤ 5 - 17
6c ≤ -12
Divide both sides by 6:
(6c)/6 ≤ (-12)/6
c ≤ -2
The solution to the inequality is c ≤ -2.
To graph the solution, we plot all values of c that are less than or equal to -2 on a number line. In other words, we shade the portion of the number line to the left or equal to -2.
Here is a graph of the solution on a number line:
<=========(-∞)==================(-2)===================
Subtract 17 from both sides:
17 + 6c - 17 ≤ 5 - 17
6c ≤ -12
Divide both sides by 6:
(6c)/6 ≤ (-12)/6
c ≤ -2
The solution to the inequality is c ≤ -2.
To graph the solution, we plot all values of c that are less than or equal to -2 on a number line. In other words, we shade the portion of the number line to the left or equal to -2.
Here is a graph of the solution on a number line:
<=========(-∞)==================(-2)===================
Solve the inequality and graph the solution. 9y–1> – 19
To solve the inequality 9y - 1 > -19, we need to isolate y.
Add 1 to both sides:
9y - 1 + 1 > -19 + 1
9y > -18
Divide both sides by 9:
(9y)/9 > (-18)/9
y > -2
The solution to the inequality is y > -2.
To graph the solution, we plot all values of y that are greater than -2 on a number line. In other words, we shade the portion of the number line to the right of -2.
Here is a graph of the solution on a number line:
<============|============(-2)=========(-∞)==================>
Add 1 to both sides:
9y - 1 + 1 > -19 + 1
9y > -18
Divide both sides by 9:
(9y)/9 > (-18)/9
y > -2
The solution to the inequality is y > -2.
To graph the solution, we plot all values of y that are greater than -2 on a number line. In other words, we shade the portion of the number line to the right of -2.
Here is a graph of the solution on a number line:
<============|============(-2)=========(-∞)==================>