Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & 7x+\frac{7}{9} \\\Leftrightarrow & 10x-\frac{4}{5}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{450}{ \color{blue}{45} }x- \frac{36}{ \color{blue}{45} })& = & (\frac{315}{ \color{blue}{45} }x+ \frac{35}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 450x \color{red}{-36} & = & \color{red}{315x} +35 \\\Leftrightarrow & 450x \color{red}{-36} \color{blue}{+36} \color{blue}{-315x} & = & \color{red}{315x} +35 \color{blue}{-315x} \color{blue}{+36} \\\Leftrightarrow & 450x-315x& = & 35+36 \\\Leftrightarrow & \color{red}{135} x& = & 71 \\\Leftrightarrow & x = \frac{71}{135} & & \\ & V = \left\{ \frac{71}{135} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{3})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 6x-\frac{4}{3}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{18}{ \color{blue}{3} }x- \frac{4}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 18x \color{red}{-4} & = & \color{red}{15x} +4 \\\Leftrightarrow & 18x \color{red}{-4} \color{blue}{+4} \color{blue}{-15x} & = & \color{red}{15x} +4 \color{blue}{-15x} \color{blue}{+4} \\\Leftrightarrow & 18x-15x& = & 4+4 \\\Leftrightarrow & \color{red}{3} x& = & 8 \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{11})& = & 9x+\frac{10}{3} \\\Leftrightarrow & 16x+\frac{16}{11}& = & 9x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{297}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+48} & = & \color{red}{297x} +110 \\\Leftrightarrow & 528x \color{red}{+48} \color{blue}{-48} \color{blue}{-297x} & = & \color{red}{297x} +110 \color{blue}{-297x} \color{blue}{-48} \\\Leftrightarrow & 528x-297x& = & 110-48 \\\Leftrightarrow & \color{red}{231} x& = & 62 \\\Leftrightarrow & x = \frac{62}{231} & & \\ & V = \left\{ \frac{62}{231} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & 8x+\frac{6}{7} \\\Leftrightarrow & 9x-\frac{12}{5}& = & 8x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-84} & = & \color{red}{280x} +30 \\\Leftrightarrow & 315x \color{red}{-84} \color{blue}{+84} \color{blue}{-280x} & = & \color{red}{280x} +30 \color{blue}{-280x} \color{blue}{+84} \\\Leftrightarrow & 315x-280x& = & 30+84 \\\Leftrightarrow & \color{red}{35} x& = & 114 \\\Leftrightarrow & x = \frac{114}{35} & & \\ & V = \left\{ \frac{114}{35} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 12x+\frac{18}{11}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{132}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 132x \color{red}{+18} & = & \color{red}{-77x} +4 \\\Leftrightarrow & 132x \color{red}{+18} \color{blue}{-18} \color{blue}{+77x} & = & \color{red}{-77x} +4 \color{blue}{+77x} \color{blue}{-18} \\\Leftrightarrow & 132x+77x& = & 4-18 \\\Leftrightarrow & \color{red}{209} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{209} & & \\ & V = \left\{ \frac{-14}{209} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{11})& = & -3x+\frac{3}{8} \\\Leftrightarrow & 20x-\frac{25}{11}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1760}{ \color{blue}{88} }x- \frac{200}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1760x \color{red}{-200} & = & \color{red}{-264x} +33 \\\Leftrightarrow & 1760x \color{red}{-200} \color{blue}{+200} \color{blue}{+264x} & = & \color{red}{-264x} +33 \color{blue}{+264x} \color{blue}{+200} \\\Leftrightarrow & 1760x+264x& = & 33+200 \\\Leftrightarrow & \color{red}{2024} x& = & 233 \\\Leftrightarrow & x = \frac{233}{2024} & & \\ & V = \left\{ \frac{233}{2024} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{3})& = & 7x+\frac{4}{9} \\\Leftrightarrow & 10x-\frac{25}{3}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{75}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-75} & = & \color{red}{63x} +4 \\\Leftrightarrow & 90x \color{red}{-75} \color{blue}{+75} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{+75} \\\Leftrightarrow & 90x-63x& = & 4+75 \\\Leftrightarrow & \color{red}{27} x& = & 79 \\\Leftrightarrow & x = \frac{79}{27} & & \\ & V = \left\{ \frac{79}{27} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{3}{8})& = & 7x+\frac{9}{7} \\\Leftrightarrow & -10x-\frac{15}{8}& = & 7x+\frac{9}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x- \frac{105}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{72}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{-105} & = & \color{red}{392x} +72 \\\Leftrightarrow & -560x \color{red}{-105} \color{blue}{+105} \color{blue}{-392x} & = & \color{red}{392x} +72 \color{blue}{-392x} \color{blue}{+105} \\\Leftrightarrow & -560x-392x& = & 72+105 \\\Leftrightarrow & \color{red}{-952} x& = & 177 \\\Leftrightarrow & x = \frac{177}{-952} & & \\\Leftrightarrow & x = \frac{-177}{952} & & \\ & V = \left\{ \frac{-177}{952} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -10x+\frac{15}{8}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-80}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -80x \color{red}{+15} & = & \color{red}{-56x} +36 \\\Leftrightarrow & -80x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +36 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -80x+56x& = & 36-15 \\\Leftrightarrow & \color{red}{-24} x& = & 21 \\\Leftrightarrow & x = \frac{21}{-24} & & \\\Leftrightarrow & x = \frac{-7}{8} & & \\ & V = \left\{ \frac{-7}{8} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{8})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 12x-\frac{9}{8}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x- \frac{27}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{64}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{-27} & = & \color{red}{120x} +64 \\\Leftrightarrow & 288x \color{red}{-27} \color{blue}{+27} \color{blue}{-120x} & = & \color{red}{120x} +64 \color{blue}{-120x} \color{blue}{+27} \\\Leftrightarrow & 288x-120x& = & 64+27 \\\Leftrightarrow & \color{red}{168} x& = & 91 \\\Leftrightarrow & x = \frac{91}{168} & & \\\Leftrightarrow & x = \frac{13}{24} & & \\ & V = \left\{ \frac{13}{24} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{2}{11} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-990}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{693}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -990x \color{red}{+88} & = & \color{red}{693x} +18 \\\Leftrightarrow & -990x \color{red}{+88} \color{blue}{-88} \color{blue}{-693x} & = & \color{red}{693x} +18 \color{blue}{-693x} \color{blue}{-88} \\\Leftrightarrow & -990x-693x& = & 18-88 \\\Leftrightarrow & \color{red}{-1683} x& = & -70 \\\Leftrightarrow & x = \frac{-70}{-1683} & & \\\Leftrightarrow & x = \frac{70}{1683} & & \\ & V = \left\{ \frac{70}{1683} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -12x+\frac{9}{10}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} })& = & (\frac{-550}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{+99} & = & \color{red}{-550x} +60 \\\Leftrightarrow & -1320x \color{red}{+99} \color{blue}{-99} \color{blue}{+550x} & = & \color{red}{-550x} +60 \color{blue}{+550x} \color{blue}{-99} \\\Leftrightarrow & -1320x+550x& = & 60-99 \\\Leftrightarrow & \color{red}{-770} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-770} & & \\\Leftrightarrow & x = \frac{39}{770} & & \\ & V = \left\{ \frac{39}{770} \right\} & \\\end{align}\)