f/–1–65≤–71
11 answers
To solve the inequality \( \frac{f}{-1} - 65 \leq -71 \), we will follow these steps:
Isolate the fraction: \[ \frac{f}{-1} - 65 \leq -71 \] Add 65 to both sides: \[ \frac{f}{-1} \leq -71 + 65 \] Simplifying the right-hand side gives: \[ \frac{f}{-1} \leq -6 \]
Multiply both sides by -1: Please remember that multiplying or dividing both sides of an inequality by a negative number reverses the inequality. Hence, \[ f \geq 6 \]
Thus, the solution is: \[ f \geq 6 \]
To solve the inequality \( -89 < t - 30 - 90 \), we will first simplify the right side of the inequality:
Combine like terms: \[ -89 < t - 30 - 90 \] Simplifying the right side: \[ -89 < t - 120 \]
Isolate \( t \): Add 120 to both sides: \[ -89 + 120 < t \] This simplifies to: \[ 31 < t \]
Rewrite the inequality: The above can be rewritten in standard form: \[ t > 31 \]
Thus, the solution is: \[ t > 31 \]
To solve the inequality \( -64 - 33p \leq -31 \), we'll follow these steps:
Isolate the term with \( p \): Start by adding 64 to both sides of the inequality: \[ -64 - 33p + 64 \leq -31 + 64 \] This simplifies to: \[ -33p \leq 33 \]
Divide by -33: When dividing both sides of an inequality by a negative number, remember to reverse the inequality sign: \[ p \geq \frac{33}{-33} \] Simplifying gives: \[ p \geq -1 \]
Thus, the solution is: \[ p \geq -1 \]
To solve the inequality \( 47 > \frac{a}{7} + 41 \), follow these steps:
Isolate the term with \( a \): Start by subtracting 41 from both sides: \[ 47 - 41 > \frac{a}{7} \] This simplifies to: \[ 6 > \frac{a}{7} \]
Multiply both sides by 7: Since 7 is positive, the direction of the inequality remains the same: \[ 6 \cdot 7 > a \] This simplifies to: \[ 42 > a \] or, equivalently, \[ a < 42 \]
Thus, the solution is: \[ a < 42 \]
To solve the inequality \( 13b + 8 \leq -5 \), follow these steps:
Isolate the term with \( b \): Start by subtracting 8 from both sides: \[ 13b + 8 - 8 \leq -5 - 8 \] This simplifies to: \[ 13b \leq -13 \]
Divide by 13: Now, divide both sides by 13. Since 13 is positive, the inequality direction remains the same: \[ b \leq \frac{-13}{13} \] This simplifies to: \[ b \leq -1 \]
Thus, the solution is: \[ b \leq -1 \]
To solve the inequality \(-79 \leq t \cdot 20 - 84\), follow these steps:
Isolate the term with \( t \): Start by adding 84 to both sides: \[ -79 + 84 \leq t \cdot 20 \] This simplifies to: \[ 5 \leq t \cdot 20 \]
Divide by 20: Now, divide both sides by 20 (since 20 is positive, the direction of the inequality remains the same): \[ \frac{5}{20} \leq t \] Simplifying gives: \[ \frac{1}{4} \leq t \] or equivalently, \[ t \geq \frac{1}{4} \]
Thus, the solution is: \[ t \geq \frac{1}{4} \]
