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Answer :
Sure! Let's solve the inequality step-by-step:
We have two separate inequalities to solve:
1. [tex]\( c - 4 > 6 \)[/tex]
2. [tex]\( 17c - 6 \leq 11 \)[/tex]
Step 1: Solve the first inequality
The inequality is:
[tex]\[ c - 4 > 6 \][/tex]
To solve for [tex]\( c \)[/tex], add 4 to both sides:
[tex]\[ c > 6 + 4 \][/tex]
This simplifies to:
[tex]\[ c > 10 \][/tex]
Step 2: Solve the second inequality
The inequality is:
[tex]\[ 17c - 6 \leq 11 \][/tex]
To solve for [tex]\( c \)[/tex], first add 6 to both sides:
[tex]\[ 17c \leq 11 + 6 \][/tex]
This simplifies to:
[tex]\[ 17c \leq 17 \][/tex]
Now, divide both sides by 17:
[tex]\[ c \leq \frac{17}{17} \][/tex]
This simplifies to:
[tex]\[ c \leq 1 \][/tex]
Step 3: Combine the solutions
The solution to the inequalities [tex]\( c - 4 > 6 \)[/tex] or [tex]\( 17c - 6 \leq 11 \)[/tex] is:
[tex]\[ c > 10 \][/tex] or [tex]\[ c \leq 1 \][/tex]
Graphing the solution:
For [tex]\( c > 10 \)[/tex], draw a number line, place an open circle at 10, and shade to the right to indicate that [tex]\( c \)[/tex] can be any number greater than 10.
For [tex]\( c \leq 1 \)[/tex], place a closed circle at 1 (indicating that 1 is included) and shade to the left to indicate that [tex]\( c \)[/tex] can be any number less than or equal to 1.
Remember, since these are combined by "or," if [tex]\( c \)[/tex] satisfies either of these inequalities, it is a solution.
We have two separate inequalities to solve:
1. [tex]\( c - 4 > 6 \)[/tex]
2. [tex]\( 17c - 6 \leq 11 \)[/tex]
Step 1: Solve the first inequality
The inequality is:
[tex]\[ c - 4 > 6 \][/tex]
To solve for [tex]\( c \)[/tex], add 4 to both sides:
[tex]\[ c > 6 + 4 \][/tex]
This simplifies to:
[tex]\[ c > 10 \][/tex]
Step 2: Solve the second inequality
The inequality is:
[tex]\[ 17c - 6 \leq 11 \][/tex]
To solve for [tex]\( c \)[/tex], first add 6 to both sides:
[tex]\[ 17c \leq 11 + 6 \][/tex]
This simplifies to:
[tex]\[ 17c \leq 17 \][/tex]
Now, divide both sides by 17:
[tex]\[ c \leq \frac{17}{17} \][/tex]
This simplifies to:
[tex]\[ c \leq 1 \][/tex]
Step 3: Combine the solutions
The solution to the inequalities [tex]\( c - 4 > 6 \)[/tex] or [tex]\( 17c - 6 \leq 11 \)[/tex] is:
[tex]\[ c > 10 \][/tex] or [tex]\[ c \leq 1 \][/tex]
Graphing the solution:
For [tex]\( c > 10 \)[/tex], draw a number line, place an open circle at 10, and shade to the right to indicate that [tex]\( c \)[/tex] can be any number greater than 10.
For [tex]\( c \leq 1 \)[/tex], place a closed circle at 1 (indicating that 1 is included) and shade to the left to indicate that [tex]\( c \)[/tex] can be any number less than or equal to 1.
Remember, since these are combined by "or," if [tex]\( c \)[/tex] satisfies either of these inequalities, it is a solution.
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Rewritten by : Barada
