To solve the inequality [tex]\( c + 5 \geq 7 \)[/tex], follow these steps:
1. Isolate the variable [tex]\( c \)[/tex]:
To get [tex]\( c \)[/tex] by itself on one side of the inequality, we need to undo the addition of 5. We can do this by subtracting 5 from both sides of the inequality. This operation will keep the inequality balanced.
[tex]\[
c + 5 - 5 \geq 7 - 5
\][/tex]
2. Simplify both sides:
On the left side, the [tex]\( +5 \)[/tex] and [tex]\(-5\)[/tex] cancel each other out, leaving us with just [tex]\( c \)[/tex]. On the right side, we perform the subtraction [tex]\( 7 - 5 \)[/tex]:
[tex]\[
c \geq 2
\][/tex]
3. Interpret the solution:
The solution to the inequality [tex]\( c + 5 \geq 7 \)[/tex] is [tex]\( c \geq 2 \)[/tex]. This means that any value of [tex]\( c \)[/tex] that is greater than or equal to 2 will satisfy the inequality.
In conclusion, the solution to the inequality [tex]\( c + 5 \geq 7 \)[/tex] is:
[tex]\[
c \geq 2
\][/tex]
