solve the inequalities 7(c-1)>6(8-3c) represent on your number line.
7(c-1)>6(8-3c)
first, get rid of the parentheses
7c-7 > 48-18c
Now collect like terms
25c > 55
Now finish it off
I don't understand it
How to solve it and get the answer
To solve the inequality 7(c-1) > 6(8-3c), we will follow these steps:
Step 1: Distribute on both sides of the inequality:
7c - 7 > 48 - 18c
Step 2: Combine like terms:
7c + 18c > 48 + 7
25c > 55
Step 3: Divide both sides of the inequality by 25 (to isolate c):
c > 55/25
Simplifying further,
c > 11/5
Now, let's represent this on a number line:
First, draw a line with an arrow indicating the positive direction.
Then, locate the value c = 11/5 (which is approximately 2.2) on the number line and mark it with an open circle (since the inequality does not include an equal sign).
Finally, draw an arrow to the right of the marked point to represent all values of c greater than 11/5.
So, the solution to the inequality 7(c-1) > 6(8-3c) on the number line is c > 11/5.
To solve the inequality 7(c-1) > 6(8-3c), we will first simplify and then solve for the variable c.
1. Distribute on both sides of the inequality:
7c - 7 > 48 - 18c
2. Collect like terms:
7c + 18c > 48 + 7
3. Combine like terms:
25c > 55
4. Divide both sides by 25:
c > 2.2
Now, we will represent the solution on a number line:
1. Draw a horizontal line and label it with numbers.
2. Mark a point on the number line to indicate c = 2.2. You can locate it between the numbers 2 and 3.
3. Since the inequality is strict (c > 2.2), we need to indicate that 2.2 is not included in the solution. This can be done by drawing an open circle (○) at 2.2.
4. Finally, draw an arrow to the right of the open circle to represent all the values of c greater than 2.2.