-7x+14>-3x-6
add 7x to each side
14> 4x-6
add 6 to each side
20>4x
divide by 4
5>x
x<5
solutions
3,0,-3,-5,-10
Answer:
All real numbers less than 5 satisfy the inequality. The set of solutions of the inequality is the interval [tex]\left(-\infty \:,\:5\right)[/tex].
Therefore, -10, -5, -3, 0, 3 are all valid solutions.
Step-by-step explanation:
Solving an inequality means finding all of its solutions. A solution of an inequality is a number which when substituted for the variable makes the inequality a true statement.
To find all the solutions for the inequality [tex]-7x+14>\:-3x-6[/tex] you must:
[tex]\mathrm{Subtract\:}14\mathrm{\:from\:both\:sides}\\-7x+14-14>-3x-6-14[/tex]
[tex]\mathrm{Simplify}\\-7x>-3x-20[/tex]
[tex]\mathrm{Add\:}3x\mathrm{\:to\:both\:sides}\\-7x+3x>-3x-20+3x[/tex]
[tex]\mathrm{Simplify}\\-4x>-20[/tex]
[tex]\mathrm{Multiply\:both\:sides\:by\:-1\:\left(reverse\:the\:inequality\right)}\\\left(-4x\right)\left(-1\right)<\left(-20\right)\left(-1\right)[/tex]
[tex]\mathrm{Simplify}\\\\4x<20\\\\\frac{4x}{4}<\frac{20}{4}\\\\x<5[/tex]
All real numbers less than 5 satisfy the inequality. The set of solutions of the inequality is the interval [tex]\left(-\infty \:,\:5\right)[/tex].
Therefore, -10, -5, -3, 0, 3 are all valid solutions.
