Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{7})& = & 9x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{20}{7}& = & 9x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{315x} +42 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{-315x} & = & \color{red}{315x} +42 \color{blue}{-315x} \color{blue}{+100} \\\Leftrightarrow & 700x-315x& = & 42+100 \\\Leftrightarrow & \color{red}{385} x& = & 142 \\\Leftrightarrow & x = \frac{142}{385} & & \\ & V = \left\{ \frac{142}{385} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{4}{7})& = & -4x+\frac{5}{6} \\\Leftrightarrow & -28x+4& = & -4x+\frac{5}{6} \\ & & & \text{kgv van noemers 1 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{24}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+24} & = & \color{red}{-24x} +5 \\\Leftrightarrow & -168x \color{red}{+24} \color{blue}{-24} \color{blue}{+24x} & = & \color{red}{-24x} +5 \color{blue}{+24x} \color{blue}{-24} \\\Leftrightarrow & -168x+24x& = & 5-24 \\\Leftrightarrow & \color{red}{-144} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-144} & & \\\Leftrightarrow & x = \frac{19}{144} & & \\ & V = \left\{ \frac{19}{144} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{11})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 14x-\frac{35}{11}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x- \frac{245}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{-245} & = & \color{red}{-231x} +33 \\\Leftrightarrow & 1078x \color{red}{-245} \color{blue}{+245} \color{blue}{+231x} & = & \color{red}{-231x} +33 \color{blue}{+231x} \color{blue}{+245} \\\Leftrightarrow & 1078x+231x& = & 33+245 \\\Leftrightarrow & \color{red}{1309} x& = & 278 \\\Leftrightarrow & x = \frac{278}{1309} & & \\ & V = \left\{ \frac{278}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{3}{2})& = & 4x+\frac{4}{11} \\\Leftrightarrow & -15x-\frac{15}{2}& = & 4x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-330}{ \color{blue}{22} }x- \frac{165}{ \color{blue}{22} })& = & (\frac{88}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -330x \color{red}{-165} & = & \color{red}{88x} +8 \\\Leftrightarrow & -330x \color{red}{-165} \color{blue}{+165} \color{blue}{-88x} & = & \color{red}{88x} +8 \color{blue}{-88x} \color{blue}{+165} \\\Leftrightarrow & -330x-88x& = & 8+165 \\\Leftrightarrow & \color{red}{-418} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-418} & & \\\Leftrightarrow & x = \frac{-173}{418} & & \\ & V = \left\{ \frac{-173}{418} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{5}{12})& = & -9x+\frac{6}{5} \\\Leftrightarrow & 14x-\frac{35}{12}& = & -9x+\frac{6}{5} \\ & & & \text{kgv van noemers 12 en 5 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{840}{ \color{blue}{60} }x- \frac{175}{ \color{blue}{60} })& = & (\frac{-540}{ \color{blue}{60} }x+ \frac{72}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & 840x \color{red}{-175} & = & \color{red}{-540x} +72 \\\Leftrightarrow & 840x \color{red}{-175} \color{blue}{+175} \color{blue}{+540x} & = & \color{red}{-540x} +72 \color{blue}{+540x} \color{blue}{+175} \\\Leftrightarrow & 840x+540x& = & 72+175 \\\Leftrightarrow & \color{red}{1380} x& = & 247 \\\Leftrightarrow & x = \frac{247}{1380} & & \\ & V = \left\{ \frac{247}{1380} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{5}{11})& = & 5x+\frac{5}{6} \\\Leftrightarrow & 8x+\frac{10}{11}& = & 5x+\frac{5}{6} \\ & & & \text{kgv van noemers 11 en 6 is 66} \\\Leftrightarrow & \color{blue}{66} .(\frac{528}{ \color{blue}{66} }x+ \frac{60}{ \color{blue}{66} })& = & (\frac{330}{ \color{blue}{66} }x+ \frac{55}{ \color{blue}{66} }). \color{blue}{66} \\\Leftrightarrow & 528x \color{red}{+60} & = & \color{red}{330x} +55 \\\Leftrightarrow & 528x \color{red}{+60} \color{blue}{-60} \color{blue}{-330x} & = & \color{red}{330x} +55 \color{blue}{-330x} \color{blue}{-60} \\\Leftrightarrow & 528x-330x& = & 55-60 \\\Leftrightarrow & \color{red}{198} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{198} & & \\ & V = \left\{ \frac{-5}{198} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{9})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-27}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{-27x} +24 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{+27x} & = & \color{red}{-27x} +24 \color{blue}{+27x} \color{blue}{-8} \\\Leftrightarrow & -72x+27x& = & 24-8 \\\Leftrightarrow & \color{red}{-45} x& = & 16 \\\Leftrightarrow & x = \frac{16}{-45} & & \\\Leftrightarrow & x = \frac{-16}{45} & & \\ & V = \left\{ \frac{-16}{45} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{-110} & = & \color{red}{-539x} +35 \\\Leftrightarrow & -770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & -770x+539x& = & 35+110 \\\Leftrightarrow & \color{red}{-231} x& = & 145 \\\Leftrightarrow & x = \frac{145}{-231} & & \\\Leftrightarrow & x = \frac{-145}{231} & & \\ & V = \left\{ \frac{-145}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{5}{7})& = & 7x+\frac{8}{3} \\\Leftrightarrow & -30x-\frac{30}{7}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-630}{ \color{blue}{21} }x- \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -630x \color{red}{-90} & = & \color{red}{147x} +56 \\\Leftrightarrow & -630x \color{red}{-90} \color{blue}{+90} \color{blue}{-147x} & = & \color{red}{147x} +56 \color{blue}{-147x} \color{blue}{+90} \\\Leftrightarrow & -630x-147x& = & 56+90 \\\Leftrightarrow & \color{red}{-777} x& = & 146 \\\Leftrightarrow & x = \frac{146}{-777} & & \\\Leftrightarrow & x = \frac{-146}{777} & & \\ & V = \left\{ \frac{-146}{777} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -4x+\frac{2}{9} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -4x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{324}{ \color{blue}{36} }x- \frac{135}{ \color{blue}{36} })& = & (\frac{-144}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 324x \color{red}{-135} & = & \color{red}{-144x} +8 \\\Leftrightarrow & 324x \color{red}{-135} \color{blue}{+135} \color{blue}{+144x} & = & \color{red}{-144x} +8 \color{blue}{+144x} \color{blue}{+135} \\\Leftrightarrow & 324x+144x& = & 8+135 \\\Leftrightarrow & \color{red}{468} x& = & 143 \\\Leftrightarrow & x = \frac{143}{468} & & \\\Leftrightarrow & x = \frac{11}{36} & & \\ & V = \left\{ \frac{11}{36} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{4}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -9x+\frac{12}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{70x} +15 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{-24} \\\Leftrightarrow & -90x-70x& = & 15-24 \\\Leftrightarrow & \color{red}{-160} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-160} & & \\\Leftrightarrow & x = \frac{9}{160} & & \\ & V = \left\{ \frac{9}{160} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{4}{3})& = & 4x+\frac{6}{11} \\\Leftrightarrow & -28x+\frac{28}{3}& = & 4x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x+ \frac{308}{ \color{blue}{33} })& = & (\frac{132}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{+308} & = & \color{red}{132x} +18 \\\Leftrightarrow & -924x \color{red}{+308} \color{blue}{-308} \color{blue}{-132x} & = & \color{red}{132x} +18 \color{blue}{-132x} \color{blue}{-308} \\\Leftrightarrow & -924x-132x& = & 18-308 \\\Leftrightarrow & \color{red}{-1056} x& = & -290 \\\Leftrightarrow & x = \frac{-290}{-1056} & & \\\Leftrightarrow & x = \frac{145}{528} & & \\ & V = \left\{ \frac{145}{528} \right\} & \\\end{align}\)