Question 117580
{{{-4(x-3) + 5 <= 3x - 7}}} 
{{{-4x +12 + 5 <= 3x - 7}}}
{{{-4x + 17 <= 3x - 7}}}
add {{{-17}}} both sides
{{{-4x <= 3x - 24}}}
add {{{-3x}}} both sides
{{{-7x <= -24}}}
multiply both sides by {{{-1}}} and reverse <
{{{7x >= 24}}}
{{{x >= 24/7}}} answer
check answer
Does {{{x = 24/7}}} solve original problem?
{{{-4(x-3) + 5 <= 3x - 7}}}
{{{-4((24/7)-3) + 5 <= 3(24/7) - 7}}}
{{{-(96/7) + 17 <= (72/7) - 7}}}
add {{{-(72/7)}}} to both sides
{{{-(168/7) + 17 <= -7}}}
{{{-(168/7) <= -24}}}
{{{-24 <= -24}}}
OK
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What if {{{x > 24/7}}}?
Make {{{x = 25/7}}}
{{{-4(x-3) + 5 <= 3x - 7}}}
{{{-4((25/7)-3) + 5 <= 3(25/7) - 7}}}
{{{-(100/7) + 17 <= (75/7) - 7}}}
{{{-(175/7) <= -24}}}
multiply by {{{-7}}} and change < to > both sides
{{{175 >= 168}}}
OK
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Now try a value outside solution set
Make {{{x = 23/7}}}
{{{-4(x-3) + 5 <= 3x - 7}}}
{{{-4((23/7)-3) + 5 <= 3(23/7) - 7}}}
{{{-(92/7) + 17 <= (69/7) - 7}}}
{{{-(161/7) + 17 <= -7}}}
{{{-(161/7) <= -24}}}
{{{161/7 >= 24}}}
{{{161 >= 168}}} Not true, {{{x = 23/7}}} does not solve
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What if we change < to >?
{{{-4(x-3) + 5 >= 3x - 7}}}
{{{-4x + 12 + 5 >= 3x - 7}}}
{{{-7x + 17 >= -7}}}
{{{-7x >= -24}}}
{{{7x <= 24}}}
{{{x <= 24/7}}} The > in answer becomes <