Question

Solve the following in equation, write down the solution set and represent it on the real numbers:
( 1 ) -2+10x ≤ 13x +10 < 24+ 10x

( X belongs to Z)​​

Answer 1

$\huge\star\underline{\mathtt\orange{❥Q} \mathfrak\blue{u }\mathfrak\blue{E} \mathbb\purple{ s}\mathtt\orange{T} \mathbb\pink{iOn}}\star\:$

• Solve the following in equation, write down the solution set and represent it on the real numbers:
• Solve the following in equation, write down the solution set and represent it on the real numbers: ( 1 ) -2+10x ≤ 13x +10 < 24+ 10x
• Solve the following in equation, write down the solution set and represent it on the real numbers: ( 1 ) -2+10x ≤ 13x +10 < 24+ 10x( X belongs to Z)

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge{\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}$

• $−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−4</u></em></strong></li><li><strong><em><u>[tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10<24+10x⇒3x<14⇒x< </u></em></strong></li><li><strong><em><u>[tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10<24+10x⇒3x<14⇒x< 3</u></em></strong></li><li><strong><em><u>[tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10<24+10x⇒3x<14⇒x< 314$
• the range of x values satisfying the above inequalities
• $is −4≤x< </u></em></strong></li><li><strong><em><u>[tex]is −4≤x< 3</u></em></strong></li><li><strong><em><u>[tex]is −4≤x< 314$

• Thus
• Thus
• Thus The number line depicting the range is shown above.

Answer 2

Answer:

Solve the following in equation, write down the solution set and represent it on the real numbers:

Solve the following in equation, write down the solution set and represent it on the real numbers: ( 1 ) -2+10x ≤ 13x +10 < 24+ 10x

Solve the following in equation, write down the solution set and represent it on the real numbers: ( 1 ) -2+10x ≤ 13x +10 < 24+ 10x( X belongs to Z)

\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \huge{\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}ANSWER!

−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−4 < /u > < /em > < /strong > < /li > < li > < strong > < em > < u > [tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10 < 24+10x⇒3x < 14⇒x < < /u > < /em > < /strong > < /li > < li > < strong > < em > < u > [tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10 < 24+10x⇒3x < 14⇒x < 3 < /u > < /em > < /strong > < /li > < li > < strong > < em > < u > [tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10 < 24+10x⇒3x < 14⇒x < 314−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−4</u></em></strong></li><li><strong><em><u>[tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10<24+10x⇒3x<14⇒x<</u></em></strong></li><li><strong><em><u>[tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10<24+10x⇒3x<14⇒x<3</u></em></strong></li><li><strong><em><u>[tex]−2+10x≤13x+10⇒−3x≤12⇒−x≤4⇒x≥−413x+10<24+10x⇒3x<14⇒x<314

the range of x values satisfying the above inequalities

is −4≤x < < /u > < /em > < /strong > < /li > < li > < strong > < em > < u > [tex]is −4≤x < 3 < /u > < /em > < /strong > < /li > < li > < strong > < em > < u > [tex]is −4≤x < 314is−4≤x<</u></em></strong></li><li><strong><em><u>[tex]is−4≤x<3</u></em></strong></li><li><strong><em><u>[tex]is−4≤x<314

Thus

Thus

Thus The number line depicting the range is shown above.