Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

1. \(-5(4x+\frac{2}{7})=7x+\frac{10}{11}\)
2. \(-3(5x+\frac{3}{7})=-4x+\frac{6}{5}\)
3. \(-6(-4x+\frac{4}{11})=-7x+\frac{3}{2}\)
4. \(5(2x+\frac{4}{11})=-3x+\frac{4}{5}\)
5. \(-4(-4x+\frac{2}{9})=-5x+\frac{6}{5}\)
6. \(5(2x+\frac{5}{6})=7x+\frac{7}{12}\)
7. \(-5(-2x+\frac{3}{4})=-9x+\frac{7}{10}\)
8. \(-4(-3x-\frac{2}{3})=7x+\frac{4}{9}\)
9. \(5(5x+\frac{5}{2})=-2x+\frac{3}{8}\)
10. \(-2(5x+\frac{4}{3})=-7x+\frac{8}{5}\)
11. \(4(-5x+\frac{4}{5})=7x+\frac{8}{9}\)
12. \(-2(-4x-\frac{2}{5})=-7x+\frac{5}{4}\)

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -20x-\frac{10}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{-110} & = & \color{red}{539x} +70 \\\Leftrightarrow & -1540x \color{red}{-110} \color{blue}{+110} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{+110} \\\Leftrightarrow & -1540x-539x& = & 70+110 \\\Leftrightarrow & \color{red}{-2079} x& = & 180 \\\Leftrightarrow & x = \frac{180}{-2079} & & \\\Leftrightarrow & x = \frac{-20}{231} & & \\ & V = \left\{ \frac{-20}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{3}{7})& = & -4x+\frac{6}{5} \\\Leftrightarrow & -15x-\frac{9}{7}& = & -4x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x- \frac{45}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{-45} & = & \color{red}{-140x} +42 \\\Leftrightarrow & -525x \color{red}{-45} \color{blue}{+45} \color{blue}{+140x} & = & \color{red}{-140x} +42 \color{blue}{+140x} \color{blue}{+45} \\\Leftrightarrow & -525x+140x& = & 42+45 \\\Leftrightarrow & \color{red}{-385} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-385} & & \\\Leftrightarrow & x = \frac{-87}{385} & & \\ & V = \left\{ \frac{-87}{385} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{11})& = & -7x+\frac{3}{2} \\\Leftrightarrow & 24x-\frac{24}{11}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{528}{ \color{blue}{22} }x- \frac{48}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 528x \color{red}{-48} & = & \color{red}{-154x} +33 \\\Leftrightarrow & 528x \color{red}{-48} \color{blue}{+48} \color{blue}{+154x} & = & \color{red}{-154x} +33 \color{blue}{+154x} \color{blue}{+48} \\\Leftrightarrow & 528x+154x& = & 33+48 \\\Leftrightarrow & \color{red}{682} x& = & 81 \\\Leftrightarrow & x = \frac{81}{682} & & \\ & V = \left\{ \frac{81}{682} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{11})& = & -3x+\frac{4}{5} \\\Leftrightarrow & 10x+\frac{20}{11}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x+ \frac{100}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{+100} & = & \color{red}{-165x} +44 \\\Leftrightarrow & 550x \color{red}{+100} \color{blue}{-100} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-100} \\\Leftrightarrow & 550x+165x& = & 44-100 \\\Leftrightarrow & \color{red}{715} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{715} & & \\ & V = \left\{ \frac{-56}{715} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 16x-\frac{8}{9}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{720}{ \color{blue}{45} }x- \frac{40}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 720x \color{red}{-40} & = & \color{red}{-225x} +54 \\\Leftrightarrow & 720x \color{red}{-40} \color{blue}{+40} \color{blue}{+225x} & = & \color{red}{-225x} +54 \color{blue}{+225x} \color{blue}{+40} \\\Leftrightarrow & 720x+225x& = & 54+40 \\\Leftrightarrow & \color{red}{945} x& = & 94 \\\Leftrightarrow & x = \frac{94}{945} & & \\ & V = \left\{ \frac{94}{945} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{5}{6})& = & 7x+\frac{7}{12} \\\Leftrightarrow & 10x+\frac{25}{6}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 6 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{120}{ \color{blue}{12} }x+ \frac{50}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{7}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 120x \color{red}{+50} & = & \color{red}{84x} +7 \\\Leftrightarrow & 120x \color{red}{+50} \color{blue}{-50} \color{blue}{-84x} & = & \color{red}{84x} +7 \color{blue}{-84x} \color{blue}{-50} \\\Leftrightarrow & 120x-84x& = & 7-50 \\\Leftrightarrow & \color{red}{36} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{36} & & \\ & V = \left\{ \frac{-43}{36} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{3}{4})& = & -9x+\frac{7}{10} \\\Leftrightarrow & 10x-\frac{15}{4}& = & -9x+\frac{7}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{200}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-180}{ \color{blue}{20} }x+ \frac{14}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 200x \color{red}{-75} & = & \color{red}{-180x} +14 \\\Leftrightarrow & 200x \color{red}{-75} \color{blue}{+75} \color{blue}{+180x} & = & \color{red}{-180x} +14 \color{blue}{+180x} \color{blue}{+75} \\\Leftrightarrow & 200x+180x& = & 14+75 \\\Leftrightarrow & \color{red}{380} x& = & 89 \\\Leftrightarrow & x = \frac{89}{380} & & \\ & V = \left\{ \frac{89}{380} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{2}{3})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 12x+\frac{8}{3}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+24} & = & \color{red}{63x} +4 \\\Leftrightarrow & 108x \color{red}{+24} \color{blue}{-24} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{-24} \\\Leftrightarrow & 108x-63x& = & 4-24 \\\Leftrightarrow & \color{red}{45} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{45} & & \\\Leftrightarrow & x = \frac{-4}{9} & & \\ & V = \left\{ \frac{-4}{9} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{2})& = & -2x+\frac{3}{8} \\\Leftrightarrow & 25x+\frac{25}{2}& = & -2x+\frac{3}{8} \\ & & & \text{kgv van noemers 2 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{200}{ \color{blue}{8} }x+ \frac{100}{ \color{blue}{8} })& = & (\frac{-16}{ \color{blue}{8} }x+ \frac{3}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 200x \color{red}{+100} & = & \color{red}{-16x} +3 \\\Leftrightarrow & 200x \color{red}{+100} \color{blue}{-100} \color{blue}{+16x} & = & \color{red}{-16x} +3 \color{blue}{+16x} \color{blue}{-100} \\\Leftrightarrow & 200x+16x& = & 3-100 \\\Leftrightarrow & \color{red}{216} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{216} & & \\ & V = \left\{ \frac{-97}{216} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-150}{ \color{blue}{15} }x- \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -150x \color{red}{-40} & = & \color{red}{-105x} +24 \\\Leftrightarrow & -150x \color{red}{-40} \color{blue}{+40} \color{blue}{+105x} & = & \color{red}{-105x} +24 \color{blue}{+105x} \color{blue}{+40} \\\Leftrightarrow & -150x+105x& = & 24+40 \\\Leftrightarrow & \color{red}{-45} x& = & 64 \\\Leftrightarrow & x = \frac{64}{-45} & & \\\Leftrightarrow & x = \frac{-64}{45} & & \\ & V = \left\{ \frac{-64}{45} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{5})& = & 7x+\frac{8}{9} \\\Leftrightarrow & -20x+\frac{16}{5}& = & 7x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-900}{ \color{blue}{45} }x+ \frac{144}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -900x \color{red}{+144} & = & \color{red}{315x} +40 \\\Leftrightarrow & -900x \color{red}{+144} \color{blue}{-144} \color{blue}{-315x} & = & \color{red}{315x} +40 \color{blue}{-315x} \color{blue}{-144} \\\Leftrightarrow & -900x-315x& = & 40-144 \\\Leftrightarrow & \color{red}{-1215} x& = & -104 \\\Leftrightarrow & x = \frac{-104}{-1215} & & \\\Leftrightarrow & x = \frac{104}{1215} & & \\ & V = \left\{ \frac{104}{1215} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{5})& = & -7x+\frac{5}{4} \\\Leftrightarrow & 8x+\frac{4}{5}& = & -7x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{160}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 160x \color{red}{+16} & = & \color{red}{-140x} +25 \\\Leftrightarrow & 160x \color{red}{+16} \color{blue}{-16} \color{blue}{+140x} & = & \color{red}{-140x} +25 \color{blue}{+140x} \color{blue}{-16} \\\Leftrightarrow & 160x+140x& = & 25-16 \\\Leftrightarrow & \color{red}{300} x& = & 9 \\\Leftrightarrow & x = \frac{9}{300} & & \\\Leftrightarrow & x = \frac{3}{100} & & \\ & V = \left\{ \frac{3}{100} \right\} & \\\end{align}\)