Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{4}{3})& = & -9x+\frac{3}{5} \\\Leftrightarrow & -8x+\frac{8}{3}& = & -9x+\frac{3}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{9}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{+40} & = & \color{red}{-135x} +9 \\\Leftrightarrow & -120x \color{red}{+40} \color{blue}{-40} \color{blue}{+135x} & = & \color{red}{-135x} +9 \color{blue}{+135x} \color{blue}{-40} \\\Leftrightarrow & -120x+135x& = & 9-40 \\\Leftrightarrow & \color{red}{15} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{15} & & \\ & V = \left\{ \frac{-31}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{4}{7})& = & 3x+\frac{9}{5} \\\Leftrightarrow & -8x+\frac{16}{7}& = & 3x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x+ \frac{80}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{+80} & = & \color{red}{105x} +63 \\\Leftrightarrow & -280x \color{red}{+80} \color{blue}{-80} \color{blue}{-105x} & = & \color{red}{105x} +63 \color{blue}{-105x} \color{blue}{-80} \\\Leftrightarrow & -280x-105x& = & 63-80 \\\Leftrightarrow & \color{red}{-385} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-385} & & \\\Leftrightarrow & x = \frac{17}{385} & & \\ & V = \left\{ \frac{17}{385} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{4}{5})& = & -2x+\frac{7}{3} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{135}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-30}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 135x \color{red}{-36} & = & \color{red}{-30x} +35 \\\Leftrightarrow & 135x \color{red}{-36} \color{blue}{+36} \color{blue}{+30x} & = & \color{red}{-30x} +35 \color{blue}{+30x} \color{blue}{+36} \\\Leftrightarrow & 135x+30x& = & 35+36 \\\Leftrightarrow & \color{red}{165} x& = & 71 \\\Leftrightarrow & x = \frac{71}{165} & & \\ & V = \left\{ \frac{71}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{4}{7})& = & -3x+\frac{8}{7} \\\Leftrightarrow & 28x+4& = & -3x+\frac{8}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{196}{ \color{blue}{7} }x+ \frac{28}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 196x \color{red}{+28} & = & \color{red}{-21x} +8 \\\Leftrightarrow & 196x \color{red}{+28} \color{blue}{-28} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-28} \\\Leftrightarrow & 196x+21x& = & 8-28 \\\Leftrightarrow & \color{red}{217} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{217} & & \\ & V = \left\{ \frac{-20}{217} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{2}{9})& = & 9x+\frac{10}{11} \\\Leftrightarrow & 8x+\frac{4}{9}& = & 9x+\frac{10}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{792}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{90}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 792x \color{red}{+44} & = & \color{red}{891x} +90 \\\Leftrightarrow & 792x \color{red}{+44} \color{blue}{-44} \color{blue}{-891x} & = & \color{red}{891x} +90 \color{blue}{-891x} \color{blue}{-44} \\\Leftrightarrow & 792x-891x& = & 90-44 \\\Leftrightarrow & \color{red}{-99} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-99} & & \\\Leftrightarrow & x = \frac{-46}{99} & & \\ & V = \left\{ \frac{-46}{99} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -2x+\frac{7}{4} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -2x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x- \frac{80}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{-80} & = & \color{red}{-24x} +21 \\\Leftrightarrow & 180x \color{red}{-80} \color{blue}{+80} \color{blue}{+24x} & = & \color{red}{-24x} +21 \color{blue}{+24x} \color{blue}{+80} \\\Leftrightarrow & 180x+24x& = & 21+80 \\\Leftrightarrow & \color{red}{204} x& = & 101 \\\Leftrightarrow & x = \frac{101}{204} & & \\ & V = \left\{ \frac{101}{204} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{11})& = & 4x+\frac{8}{9} \\\Leftrightarrow & -28x+\frac{35}{11}& = & 4x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2772}{ \color{blue}{99} }x+ \frac{315}{ \color{blue}{99} })& = & (\frac{396}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2772x \color{red}{+315} & = & \color{red}{396x} +88 \\\Leftrightarrow & -2772x \color{red}{+315} \color{blue}{-315} \color{blue}{-396x} & = & \color{red}{396x} +88 \color{blue}{-396x} \color{blue}{-315} \\\Leftrightarrow & -2772x-396x& = & 88-315 \\\Leftrightarrow & \color{red}{-3168} x& = & -227 \\\Leftrightarrow & x = \frac{-227}{-3168} & & \\\Leftrightarrow & x = \frac{227}{3168} & & \\ & V = \left\{ \frac{227}{3168} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{3}{5})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -8x-\frac{12}{5}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -280x \color{red}{-84} & = & \color{red}{105x} +20 \\\Leftrightarrow & -280x \color{red}{-84} \color{blue}{+84} \color{blue}{-105x} & = & \color{red}{105x} +20 \color{blue}{-105x} \color{blue}{+84} \\\Leftrightarrow & -280x-105x& = & 20+84 \\\Leftrightarrow & \color{red}{-385} x& = & 104 \\\Leftrightarrow & x = \frac{104}{-385} & & \\\Leftrightarrow & x = \frac{-104}{385} & & \\ & V = \left\{ \frac{-104}{385} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{3})& = & 9x+\frac{6}{7} \\\Leftrightarrow & 4x-\frac{8}{3}& = & 9x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{84}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 84x \color{red}{-56} & = & \color{red}{189x} +18 \\\Leftrightarrow & 84x \color{red}{-56} \color{blue}{+56} \color{blue}{-189x} & = & \color{red}{189x} +18 \color{blue}{-189x} \color{blue}{+56} \\\Leftrightarrow & 84x-189x& = & 18+56 \\\Leftrightarrow & \color{red}{-105} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-105} & & \\\Leftrightarrow & x = \frac{-74}{105} & & \\ & V = \left\{ \frac{-74}{105} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{3}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -28x+\frac{21}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-308}{ \color{blue}{11} }x+ \frac{21}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -308x \color{red}{+21} & = & \color{red}{-99x} +6 \\\Leftrightarrow & -308x \color{red}{+21} \color{blue}{-21} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{-21} \\\Leftrightarrow & -308x+99x& = & 6-21 \\\Leftrightarrow & \color{red}{-209} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-209} & & \\\Leftrightarrow & x = \frac{15}{209} & & \\ & V = \left\{ \frac{15}{209} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{2}{5})& = & -8x+\frac{4}{7} \\\Leftrightarrow & -15x+\frac{6}{5}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-525}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -525x \color{red}{+42} & = & \color{red}{-280x} +20 \\\Leftrightarrow & -525x \color{red}{+42} \color{blue}{-42} \color{blue}{+280x} & = & \color{red}{-280x} +20 \color{blue}{+280x} \color{blue}{-42} \\\Leftrightarrow & -525x+280x& = & 20-42 \\\Leftrightarrow & \color{red}{-245} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-245} & & \\\Leftrightarrow & x = \frac{22}{245} & & \\ & V = \left\{ \frac{22}{245} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{5}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & -20x-\frac{25}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-840}{ \color{blue}{42} }x- \frac{150}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -840x \color{red}{-150} & = & \color{red}{-294x} +35 \\\Leftrightarrow & -840x \color{red}{-150} \color{blue}{+150} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{+150} \\\Leftrightarrow & -840x+294x& = & 35+150 \\\Leftrightarrow & \color{red}{-546} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-546} & & \\\Leftrightarrow & x = \frac{-185}{546} & & \\ & V = \left\{ \frac{-185}{546} \right\} & \\\end{align}\)