Solve the following polynomial inequalities.
4x - 5 ≤ 2(x - 7)
4 x - 5 ¡Ü 2( x - 7 )
4 x - 5 ¡Ü 2 * x - 2 * 7
4 x - 5 ¡Ü 2 x - 14 Add - 2 x to both sides
4 x - 2 x - 5 ¡Ü 2 x - 14 - 2 x
2 x - 5 ¡Ü - 14 Add 5 to both sides
2 x - 5 + 5 ¡Ü - 14 + 5
2 x ¡Ü - 9 Divide both sides by 2
x ¡Ü - 9 / 2
¡Ü
mean less or equal
To solve the given polynomial inequality: 4x - 5 ≤ 2(x - 7), we need to simplify the expressions and isolate the variable.
Let's start by distributing the 2 on the right side of the inequality:
4x - 5 ≤ 2x - 14
Now, we can combine like terms by subtracting 2x from both sides:
2x - 5 ≤ -14
Next, we will isolate the variable x by adding 5 to both sides:
2x ≤ -14 + 5
2x ≤ -9
Finally, we divide both sides of the inequality by 2 since the coefficient of x is 2 and it is positive (if it were negative, we would need to flip the inequality):
x ≤ -9/2
Therefore, the solution to the inequality 4x - 5 ≤ 2(x - 7) is x ≤ -9/2.