Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{4}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -30x+\frac{24}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{24}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+24} & = & \color{red}{49x} +3 \\\Leftrightarrow & -210x \color{red}{+24} \color{blue}{-24} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-24} \\\Leftrightarrow & -210x-49x& = & 3-24 \\\Leftrightarrow & \color{red}{-259} x& = & -21 \\\Leftrightarrow & x = \frac{-21}{-259} & & \\\Leftrightarrow & x = \frac{3}{37} & & \\ & V = \left\{ \frac{3}{37} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{3}{7})& = & 7x+\frac{3}{11} \\\Leftrightarrow & -6x+\frac{6}{7}& = & 7x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+66} & = & \color{red}{539x} +21 \\\Leftrightarrow & -462x \color{red}{+66} \color{blue}{-66} \color{blue}{-539x} & = & \color{red}{539x} +21 \color{blue}{-539x} \color{blue}{-66} \\\Leftrightarrow & -462x-539x& = & 21-66 \\\Leftrightarrow & \color{red}{-1001} x& = & -45 \\\Leftrightarrow & x = \frac{-45}{-1001} & & \\\Leftrightarrow & x = \frac{45}{1001} & & \\ & V = \left\{ \frac{45}{1001} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{2})& = & 4x+\frac{8}{3} \\\Leftrightarrow & -35x-\frac{35}{2}& = & 4x+\frac{8}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-210}{ \color{blue}{6} }x- \frac{105}{ \color{blue}{6} })& = & (\frac{24}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -210x \color{red}{-105} & = & \color{red}{24x} +16 \\\Leftrightarrow & -210x \color{red}{-105} \color{blue}{+105} \color{blue}{-24x} & = & \color{red}{24x} +16 \color{blue}{-24x} \color{blue}{+105} \\\Leftrightarrow & -210x-24x& = & 16+105 \\\Leftrightarrow & \color{red}{-234} x& = & 121 \\\Leftrightarrow & x = \frac{121}{-234} & & \\\Leftrightarrow & x = \frac{-121}{234} & & \\ & V = \left\{ \frac{-121}{234} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{5}{8})& = & -7x+\frac{3}{7} \\\Leftrightarrow & 20x+\frac{25}{8}& = & -7x+\frac{3}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x+ \frac{175}{ \color{blue}{56} })& = & (\frac{-392}{ \color{blue}{56} }x+ \frac{24}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{+175} & = & \color{red}{-392x} +24 \\\Leftrightarrow & 1120x \color{red}{+175} \color{blue}{-175} \color{blue}{+392x} & = & \color{red}{-392x} +24 \color{blue}{+392x} \color{blue}{-175} \\\Leftrightarrow & 1120x+392x& = & 24-175 \\\Leftrightarrow & \color{red}{1512} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{1512} & & \\ & V = \left\{ \frac{-151}{1512} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{2}{5})& = & 6x+\frac{8}{3} \\\Leftrightarrow & -18x+\frac{12}{5}& = & 6x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-270}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{90}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -270x \color{red}{+36} & = & \color{red}{90x} +40 \\\Leftrightarrow & -270x \color{red}{+36} \color{blue}{-36} \color{blue}{-90x} & = & \color{red}{90x} +40 \color{blue}{-90x} \color{blue}{-36} \\\Leftrightarrow & -270x-90x& = & 40-36 \\\Leftrightarrow & \color{red}{-360} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-360} & & \\\Leftrightarrow & x = \frac{-1}{90} & & \\ & V = \left\{ \frac{-1}{90} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{11})& = & 7x+\frac{6}{7} \\\Leftrightarrow & 20x+\frac{8}{11}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1540}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1540x \color{red}{+56} & = & \color{red}{539x} +66 \\\Leftrightarrow & 1540x \color{red}{+56} \color{blue}{-56} \color{blue}{-539x} & = & \color{red}{539x} +66 \color{blue}{-539x} \color{blue}{-56} \\\Leftrightarrow & 1540x-539x& = & 66-56 \\\Leftrightarrow & \color{red}{1001} x& = & 10 \\\Leftrightarrow & x = \frac{10}{1001} & & \\ & V = \left\{ \frac{10}{1001} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{5}{7})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 18x-\frac{30}{7}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-150} & = & \color{red}{175x} +56 \\\Leftrightarrow & 630x \color{red}{-150} \color{blue}{+150} \color{blue}{-175x} & = & \color{red}{175x} +56 \color{blue}{-175x} \color{blue}{+150} \\\Leftrightarrow & 630x-175x& = & 56+150 \\\Leftrightarrow & \color{red}{455} x& = & 206 \\\Leftrightarrow & x = \frac{206}{455} & & \\ & V = \left\{ \frac{206}{455} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{3}{11})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 30x-\frac{18}{11}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1320}{ \color{blue}{44} }x- \frac{72}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1320x \color{red}{-72} & = & \color{red}{308x} +99 \\\Leftrightarrow & 1320x \color{red}{-72} \color{blue}{+72} \color{blue}{-308x} & = & \color{red}{308x} +99 \color{blue}{-308x} \color{blue}{+72} \\\Leftrightarrow & 1320x-308x& = & 99+72 \\\Leftrightarrow & \color{red}{1012} x& = & 171 \\\Leftrightarrow & x = \frac{171}{1012} & & \\ & V = \left\{ \frac{171}{1012} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{4}{3})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -10x+\frac{8}{3}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-60}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} })& = & (\frac{-42}{ \color{blue}{6} }x+ \frac{9}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -60x \color{red}{+16} & = & \color{red}{-42x} +9 \\\Leftrightarrow & -60x \color{red}{+16} \color{blue}{-16} \color{blue}{+42x} & = & \color{red}{-42x} +9 \color{blue}{+42x} \color{blue}{-16} \\\Leftrightarrow & -60x+42x& = & 9-16 \\\Leftrightarrow & \color{red}{-18} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{-18} & & \\\Leftrightarrow & x = \frac{7}{18} & & \\ & V = \left\{ \frac{7}{18} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{3}{8})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -21x+\frac{21}{8}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-1176}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -1176x \color{red}{+147} & = & \color{red}{-448x} +32 \\\Leftrightarrow & -1176x \color{red}{+147} \color{blue}{-147} \color{blue}{+448x} & = & \color{red}{-448x} +32 \color{blue}{+448x} \color{blue}{-147} \\\Leftrightarrow & -1176x+448x& = & 32-147 \\\Leftrightarrow & \color{red}{-728} x& = & -115 \\\Leftrightarrow & x = \frac{-115}{-728} & & \\\Leftrightarrow & x = \frac{115}{728} & & \\ & V = \left\{ \frac{115}{728} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{24}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x- \frac{72}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{-72} & = & \color{red}{-231x} +88 \\\Leftrightarrow & -792x \color{red}{-72} \color{blue}{+72} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{+72} \\\Leftrightarrow & -792x+231x& = & 88+72 \\\Leftrightarrow & \color{red}{-561} x& = & 160 \\\Leftrightarrow & x = \frac{160}{-561} & & \\\Leftrightarrow & x = \frac{-160}{561} & & \\ & V = \left\{ \frac{-160}{561} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{5}{9})& = & 3x+\frac{9}{10} \\\Leftrightarrow & -35x-\frac{35}{9}& = & 3x+\frac{9}{10} \\ & & & \text{kgv van noemers 9 en 10 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{-3150}{ \color{blue}{90} }x- \frac{350}{ \color{blue}{90} })& = & (\frac{270}{ \color{blue}{90} }x+ \frac{81}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & -3150x \color{red}{-350} & = & \color{red}{270x} +81 \\\Leftrightarrow & -3150x \color{red}{-350} \color{blue}{+350} \color{blue}{-270x} & = & \color{red}{270x} +81 \color{blue}{-270x} \color{blue}{+350} \\\Leftrightarrow & -3150x-270x& = & 81+350 \\\Leftrightarrow & \color{red}{-3420} x& = & 431 \\\Leftrightarrow & x = \frac{431}{-3420} & & \\\Leftrightarrow & x = \frac{-431}{3420} & & \\ & V = \left\{ \frac{-431}{3420} \right\} & \\\end{align}\)