Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & 9x+\frac{6}{11} \\\Leftrightarrow & -8x+\frac{8}{9}& = & 9x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-792}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -792x \color{red}{+88} & = & \color{red}{891x} +54 \\\Leftrightarrow & -792x \color{red}{+88} \color{blue}{-88} \color{blue}{-891x} & = & \color{red}{891x} +54 \color{blue}{-891x} \color{blue}{-88} \\\Leftrightarrow & -792x-891x& = & 54-88 \\\Leftrightarrow & \color{red}{-1683} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-1683} & & \\\Leftrightarrow & x = \frac{2}{99} & & \\ & V = \left\{ \frac{2}{99} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & 9x+\frac{5}{7} \\\Leftrightarrow & -8x+\frac{10}{7}& = & 9x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-56}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{63}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -56x \color{red}{+10} & = & \color{red}{63x} +5 \\\Leftrightarrow & -56x \color{red}{+10} \color{blue}{-10} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{-10} \\\Leftrightarrow & -56x-63x& = & 5-10 \\\Leftrightarrow & \color{red}{-119} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-119} & & \\\Leftrightarrow & x = \frac{5}{119} & & \\ & V = \left\{ \frac{5}{119} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{4}{5})& = & 4x+\frac{9}{2} \\\Leftrightarrow & -15x+\frac{12}{5}& = & 4x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+24} & = & \color{red}{40x} +45 \\\Leftrightarrow & -150x \color{red}{+24} \color{blue}{-24} \color{blue}{-40x} & = & \color{red}{40x} +45 \color{blue}{-40x} \color{blue}{-24} \\\Leftrightarrow & -150x-40x& = & 45-24 \\\Leftrightarrow & \color{red}{-190} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-190} & & \\\Leftrightarrow & x = \frac{-21}{190} & & \\ & V = \left\{ \frac{-21}{190} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{5})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+12} & = & \color{red}{-105x} +20 \\\Leftrightarrow & -90x \color{red}{+12} \color{blue}{-12} \color{blue}{+105x} & = & \color{red}{-105x} +20 \color{blue}{+105x} \color{blue}{-12} \\\Leftrightarrow & -90x+105x& = & 20-12 \\\Leftrightarrow & \color{red}{15} x& = & 8 \\\Leftrightarrow & x = \frac{8}{15} & & \\ & V = \left\{ \frac{8}{15} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{5}{3})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -16x+\frac{20}{3}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{+220} & = & \color{red}{-231x} +15 \\\Leftrightarrow & -528x \color{red}{+220} \color{blue}{-220} \color{blue}{+231x} & = & \color{red}{-231x} +15 \color{blue}{+231x} \color{blue}{-220} \\\Leftrightarrow & -528x+231x& = & 15-220 \\\Leftrightarrow & \color{red}{-297} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-297} & & \\\Leftrightarrow & x = \frac{205}{297} & & \\ & V = \left\{ \frac{205}{297} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 5x+\frac{7}{5} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 5x+\frac{7}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{30}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{49}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-30} & = & \color{red}{175x} +49 \\\Leftrightarrow & 210x \color{red}{-30} \color{blue}{+30} \color{blue}{-175x} & = & \color{red}{175x} +49 \color{blue}{-175x} \color{blue}{+30} \\\Leftrightarrow & 210x-175x& = & 49+30 \\\Leftrightarrow & \color{red}{35} x& = & 79 \\\Leftrightarrow & x = \frac{79}{35} & & \\ & V = \left\{ \frac{79}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+30} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 280x \color{red}{+30} \color{blue}{-30} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{-30} \\\Leftrightarrow & 280x+105x& = & 42-30 \\\Leftrightarrow & \color{red}{385} x& = & 12 \\\Leftrightarrow & x = \frac{12}{385} & & \\ & V = \left\{ \frac{12}{385} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{20}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+60} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -252x \color{red}{+60} \color{blue}{-60} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-60} \\\Leftrightarrow & -252x+105x& = & 56-60 \\\Leftrightarrow & \color{red}{-147} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-147} & & \\\Leftrightarrow & x = \frac{4}{147} & & \\ & V = \left\{ \frac{4}{147} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & 5x+\frac{8}{11} \\\Leftrightarrow & -4x-\frac{6}{7}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-66} & = & \color{red}{385x} +56 \\\Leftrightarrow & -308x \color{red}{-66} \color{blue}{+66} \color{blue}{-385x} & = & \color{red}{385x} +56 \color{blue}{-385x} \color{blue}{+66} \\\Leftrightarrow & -308x-385x& = & 56+66 \\\Leftrightarrow & \color{red}{-693} x& = & 122 \\\Leftrightarrow & x = \frac{122}{-693} & & \\\Leftrightarrow & x = \frac{-122}{693} & & \\ & V = \left\{ \frac{-122}{693} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{11})& = & 7x+\frac{7}{8} \\\Leftrightarrow & 10x+\frac{10}{11}& = & 7x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{880}{ \color{blue}{88} }x+ \frac{80}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 880x \color{red}{+80} & = & \color{red}{616x} +77 \\\Leftrightarrow & 880x \color{red}{+80} \color{blue}{-80} \color{blue}{-616x} & = & \color{red}{616x} +77 \color{blue}{-616x} \color{blue}{-80} \\\Leftrightarrow & 880x-616x& = & 77-80 \\\Leftrightarrow & \color{red}{264} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{264} & & \\\Leftrightarrow & x = \frac{-1}{88} & & \\ & V = \left\{ \frac{-1}{88} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{5}{3})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -12x-\frac{20}{3}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 3 en 12 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{5}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-80} & = & \color{red}{60x} +5 \\\Leftrightarrow & -144x \color{red}{-80} \color{blue}{+80} \color{blue}{-60x} & = & \color{red}{60x} +5 \color{blue}{-60x} \color{blue}{+80} \\\Leftrightarrow & -144x-60x& = & 5+80 \\\Leftrightarrow & \color{red}{-204} x& = & 85 \\\Leftrightarrow & x = \frac{85}{-204} & & \\\Leftrightarrow & x = \frac{-5}{12} & & \\ & V = \left\{ \frac{-5}{12} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{4})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 6x+\frac{9}{4}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{216}{ \color{blue}{36} }x+ \frac{81}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{20}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 216x \color{red}{+81} & = & \color{red}{-180x} +20 \\\Leftrightarrow & 216x \color{red}{+81} \color{blue}{-81} \color{blue}{+180x} & = & \color{red}{-180x} +20 \color{blue}{+180x} \color{blue}{-81} \\\Leftrightarrow & 216x+180x& = & 20-81 \\\Leftrightarrow & \color{red}{396} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{396} & & \\ & V = \left\{ \frac{-61}{396} \right\} & \\\end{align}\)