Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+2)& = & -8x+\frac{8}{3} \\\Leftrightarrow & -21x-14& = & -8x+\frac{8}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-63}{ \color{blue}{3} }x- \frac{42}{ \color{blue}{3} })& = & (\frac{-24}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -63x \color{red}{-42} & = & \color{red}{-24x} +8 \\\Leftrightarrow & -63x \color{red}{-42} \color{blue}{+42} \color{blue}{+24x} & = & \color{red}{-24x} +8 \color{blue}{+24x} \color{blue}{+42} \\\Leftrightarrow & -63x+24x& = & 8+42 \\\Leftrightarrow & \color{red}{-39} x& = & 50 \\\Leftrightarrow & x = \frac{50}{-39} & & \\\Leftrightarrow & x = \frac{-50}{39} & & \\ & V = \left\{ \frac{-50}{39} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{-36} & = & \color{red}{75x} +50 \\\Leftrightarrow & -180x \color{red}{-36} \color{blue}{+36} \color{blue}{-75x} & = & \color{red}{75x} +50 \color{blue}{-75x} \color{blue}{+36} \\\Leftrightarrow & -180x-75x& = & 50+36 \\\Leftrightarrow & \color{red}{-255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{-255} & & \\\Leftrightarrow & x = \frac{-86}{255} & & \\ & V = \left\{ \frac{-86}{255} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+84} & = & \color{red}{175x} +50 \\\Leftrightarrow & -420x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & -420x-175x& = & 50-84 \\\Leftrightarrow & \color{red}{-595} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{-595} & & \\\Leftrightarrow & x = \frac{2}{35} & & \\ & V = \left\{ \frac{2}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{1}{2})& = & -8x+\frac{4}{3} \\\Leftrightarrow & -15x+\frac{5}{2}& = & -8x+\frac{4}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-90}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} })& = & (\frac{-48}{ \color{blue}{6} }x+ \frac{8}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -90x \color{red}{+15} & = & \color{red}{-48x} +8 \\\Leftrightarrow & -90x \color{red}{+15} \color{blue}{-15} \color{blue}{+48x} & = & \color{red}{-48x} +8 \color{blue}{+48x} \color{blue}{-15} \\\Leftrightarrow & -90x+48x& = & 8-15 \\\Leftrightarrow & \color{red}{-42} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-42} & & \\\Leftrightarrow & x = \frac{1}{6} & & \\ & V = \left\{ \frac{1}{6} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{7})& = & -5x+\frac{9}{5} \\\Leftrightarrow & 6x-\frac{10}{7}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x- \frac{50}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{-50} & = & \color{red}{-175x} +63 \\\Leftrightarrow & 210x \color{red}{-50} \color{blue}{+50} \color{blue}{+175x} & = & \color{red}{-175x} +63 \color{blue}{+175x} \color{blue}{+50} \\\Leftrightarrow & 210x+175x& = & 63+50 \\\Leftrightarrow & \color{red}{385} x& = & 113 \\\Leftrightarrow & x = \frac{113}{385} & & \\ & V = \left\{ \frac{113}{385} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{5})& = & 3x+\frac{7}{2} \\\Leftrightarrow & -14x+\frac{28}{5}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-140}{ \color{blue}{10} }x+ \frac{56}{ \color{blue}{10} })& = & (\frac{30}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -140x \color{red}{+56} & = & \color{red}{30x} +35 \\\Leftrightarrow & -140x \color{red}{+56} \color{blue}{-56} \color{blue}{-30x} & = & \color{red}{30x} +35 \color{blue}{-30x} \color{blue}{-56} \\\Leftrightarrow & -140x-30x& = & 35-56 \\\Leftrightarrow & \color{red}{-170} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-170} & & \\\Leftrightarrow & x = \frac{21}{170} & & \\ & V = \left\{ \frac{21}{170} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{3}{7})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 4x+\frac{6}{7}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{54}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+54} & = & \color{red}{441x} +28 \\\Leftrightarrow & 252x \color{red}{+54} \color{blue}{-54} \color{blue}{-441x} & = & \color{red}{441x} +28 \color{blue}{-441x} \color{blue}{-54} \\\Leftrightarrow & 252x-441x& = & 28-54 \\\Leftrightarrow & \color{red}{-189} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-189} & & \\\Leftrightarrow & x = \frac{26}{189} & & \\ & V = \left\{ \frac{26}{189} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{5}{9})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 4x-\frac{10}{9}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{72}{ \color{blue}{18} }x- \frac{20}{ \color{blue}{18} })& = & (\frac{-90}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 72x \color{red}{-20} & = & \color{red}{-90x} +81 \\\Leftrightarrow & 72x \color{red}{-20} \color{blue}{+20} \color{blue}{+90x} & = & \color{red}{-90x} +81 \color{blue}{+90x} \color{blue}{+20} \\\Leftrightarrow & 72x+90x& = & 81+20 \\\Leftrightarrow & \color{red}{162} x& = & 101 \\\Leftrightarrow & x = \frac{101}{162} & & \\ & V = \left\{ \frac{101}{162} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{3})& = & -9x+\frac{4}{3} \\\Leftrightarrow & 16x-\frac{20}{3}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{-27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{-20} & = & \color{red}{-27x} +4 \\\Leftrightarrow & 48x \color{red}{-20} \color{blue}{+20} \color{blue}{+27x} & = & \color{red}{-27x} +4 \color{blue}{+27x} \color{blue}{+20} \\\Leftrightarrow & 48x+27x& = & 4+20 \\\Leftrightarrow & \color{red}{75} x& = & 24 \\\Leftrightarrow & x = \frac{24}{75} & & \\\Leftrightarrow & x = \frac{8}{25} & & \\ & V = \left\{ \frac{8}{25} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{4}{11})& = & -9x+\frac{7}{8} \\\Leftrightarrow & 16x-\frac{16}{11}& = & -9x+\frac{7}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1408}{ \color{blue}{88} }x- \frac{128}{ \color{blue}{88} })& = & (\frac{-792}{ \color{blue}{88} }x+ \frac{77}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1408x \color{red}{-128} & = & \color{red}{-792x} +77 \\\Leftrightarrow & 1408x \color{red}{-128} \color{blue}{+128} \color{blue}{+792x} & = & \color{red}{-792x} +77 \color{blue}{+792x} \color{blue}{+128} \\\Leftrightarrow & 1408x+792x& = & 77+128 \\\Leftrightarrow & \color{red}{2200} x& = & 205 \\\Leftrightarrow & x = \frac{205}{2200} & & \\\Leftrightarrow & x = \frac{41}{440} & & \\ & V = \left\{ \frac{41}{440} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{4}{11})& = & -5x+\frac{10}{3} \\\Leftrightarrow & -12x-\frac{24}{11}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-72} & = & \color{red}{-165x} +110 \\\Leftrightarrow & -396x \color{red}{-72} \color{blue}{+72} \color{blue}{+165x} & = & \color{red}{-165x} +110 \color{blue}{+165x} \color{blue}{+72} \\\Leftrightarrow & -396x+165x& = & 110+72 \\\Leftrightarrow & \color{red}{-231} x& = & 182 \\\Leftrightarrow & x = \frac{182}{-231} & & \\\Leftrightarrow & x = \frac{-26}{33} & & \\ & V = \left\{ \frac{-26}{33} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & 2x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 2x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-36} & = & \color{red}{30x} +10 \\\Leftrightarrow & 135x \color{red}{-36} \color{blue}{+36} \color{blue}{-30x} & = & \color{red}{30x} +10 \color{blue}{-30x} \color{blue}{+36} \\\Leftrightarrow & 135x-30x& = & 10+36 \\\Leftrightarrow & \color{red}{105} x& = & 46 \\\Leftrightarrow & x = \frac{46}{105} & & \\ & V = \left\{ \frac{46}{105} \right\} & \\\end{align}\)