10. 5 (2r 7) 3 (2x +3) s0, 2x 19 s6x47
The given inequality is
5 ( 2 x − 7 ) − 3 ( 2 x + 3 ) ≤ 0 (1).
2 x + 19 ≤ 6 x + 4 (2)
Solve the inequality (1)
5 ( 2 x − 7 ) − 3 ( 2 x + 3 ) ≤ 0 10 x − 35 − 6 x + 9 ≤ 0 4 x − 44 ≤ 0 x ≤ 44 4
Further simplify the inequality (1)
x > 11 (3)
Solve the inequality (2)
2 x + 19 ≤ 6 x + 47 2 x − 6 x ≤ 47 − 19 − 4 x ≤ 28 − x ≤ 7 (4)
As there is a negative sign on x in equation (4), so we need to multiply it by -1.
Further simplify the inequality (2)
( − 1 ) ( − x ) ≥ ( − 1 ) ( 7 ) x ≥ − 7 (5)
Consider both (3) and (5) inequalities together.
x > 11 and x ≥ − 7
The graphical representation of the solution is shown below:
The given inequality is
Solve the inequality (1)
Further simplify the inequality (1)
Solve the inequality (2)
As there is a negative sign on x in equation (4), so we need to multiply it by -1.
Further simplify the inequality (2)
Consider both (3) and (5) inequalities together.
The graphical representation of the solution is shown below:
