Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{5})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -6x+\frac{9}{5}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x+ \frac{27}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{+27} & = & \color{red}{-105x} +50 \\\Leftrightarrow & -90x \color{red}{+27} \color{blue}{-27} \color{blue}{+105x} & = & \color{red}{-105x} +50 \color{blue}{+105x} \color{blue}{-27} \\\Leftrightarrow & -90x+105x& = & 50-27 \\\Leftrightarrow & \color{red}{15} x& = & 23 \\\Leftrightarrow & x = \frac{23}{15} & & \\ & V = \left\{ \frac{23}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{11})& = & 4x+\frac{9}{11} \\\Leftrightarrow & -15x-\frac{10}{11}& = & 4x+\frac{9}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-165}{ \color{blue}{11} }x- \frac{10}{ \color{blue}{11} })& = & (\frac{44}{ \color{blue}{11} }x+ \frac{9}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -165x \color{red}{-10} & = & \color{red}{44x} +9 \\\Leftrightarrow & -165x \color{red}{-10} \color{blue}{+10} \color{blue}{-44x} & = & \color{red}{44x} +9 \color{blue}{-44x} \color{blue}{+10} \\\Leftrightarrow & -165x-44x& = & 9+10 \\\Leftrightarrow & \color{red}{-209} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-209} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{11})& = & -2x+\frac{7}{3} \\\Leftrightarrow & 9x+\frac{12}{11}& = & -2x+\frac{7}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x+ \frac{36}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{77}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{+36} & = & \color{red}{-66x} +77 \\\Leftrightarrow & 297x \color{red}{+36} \color{blue}{-36} \color{blue}{+66x} & = & \color{red}{-66x} +77 \color{blue}{+66x} \color{blue}{-36} \\\Leftrightarrow & 297x+66x& = & 77-36 \\\Leftrightarrow & \color{red}{363} x& = & 41 \\\Leftrightarrow & x = \frac{41}{363} & & \\ & V = \left\{ \frac{41}{363} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -9x-\frac{6}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-495}{ \color{blue}{55} }x- \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -495x \color{red}{-66} & = & \color{red}{275x} +10 \\\Leftrightarrow & -495x \color{red}{-66} \color{blue}{+66} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{+66} \\\Leftrightarrow & -495x-275x& = & 10+66 \\\Leftrightarrow & \color{red}{-770} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-770} & & \\\Leftrightarrow & x = \frac{-38}{385} & & \\ & V = \left\{ \frac{-38}{385} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{4}{11})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 20x-\frac{20}{11}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{220}{ \color{blue}{11} }x- \frac{20}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 220x \color{red}{-20} & = & \color{red}{-99x} +6 \\\Leftrightarrow & 220x \color{red}{-20} \color{blue}{+20} \color{blue}{+99x} & = & \color{red}{-99x} +6 \color{blue}{+99x} \color{blue}{+20} \\\Leftrightarrow & 220x+99x& = & 6+20 \\\Leftrightarrow & \color{red}{319} x& = & 26 \\\Leftrightarrow & x = \frac{26}{319} & & \\ & V = \left\{ \frac{26}{319} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{11})& = & -7x+\frac{10}{3} \\\Leftrightarrow & -10x-\frac{25}{11}& = & -7x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-330}{ \color{blue}{33} }x- \frac{75}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -330x \color{red}{-75} & = & \color{red}{-231x} +110 \\\Leftrightarrow & -330x \color{red}{-75} \color{blue}{+75} \color{blue}{+231x} & = & \color{red}{-231x} +110 \color{blue}{+231x} \color{blue}{+75} \\\Leftrightarrow & -330x+231x& = & 110+75 \\\Leftrightarrow & \color{red}{-99} x& = & 185 \\\Leftrightarrow & x = \frac{185}{-99} & & \\\Leftrightarrow & x = \frac{-185}{99} & & \\ & V = \left\{ \frac{-185}{99} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{11})& = & -9x+\frac{10}{11} \\\Leftrightarrow & -8x-\frac{6}{11}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-88}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-99}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -88x \color{red}{-6} & = & \color{red}{-99x} +10 \\\Leftrightarrow & -88x \color{red}{-6} \color{blue}{+6} \color{blue}{+99x} & = & \color{red}{-99x} +10 \color{blue}{+99x} \color{blue}{+6} \\\Leftrightarrow & -88x+99x& = & 10+6 \\\Leftrightarrow & \color{red}{11} x& = & 16 \\\Leftrightarrow & x = \frac{16}{11} & & \\ & V = \left\{ \frac{16}{11} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{30}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-30} & = & \color{red}{99x} +88 \\\Leftrightarrow & 330x \color{red}{-30} \color{blue}{+30} \color{blue}{-99x} & = & \color{red}{99x} +88 \color{blue}{-99x} \color{blue}{+30} \\\Leftrightarrow & 330x-99x& = & 88+30 \\\Leftrightarrow & \color{red}{231} x& = & 118 \\\Leftrightarrow & x = \frac{118}{231} & & \\ & V = \left\{ \frac{118}{231} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{4}{7})& = & -9x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x- \frac{176}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{-176} & = & \color{red}{-693x} +35 \\\Leftrightarrow & 616x \color{red}{-176} \color{blue}{+176} \color{blue}{+693x} & = & \color{red}{-693x} +35 \color{blue}{+693x} \color{blue}{+176} \\\Leftrightarrow & 616x+693x& = & 35+176 \\\Leftrightarrow & \color{red}{1309} x& = & 211 \\\Leftrightarrow & x = \frac{211}{1309} & & \\ & V = \left\{ \frac{211}{1309} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x-\frac{1}{2})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 28x+\frac{7}{2}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{168}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 168x \color{red}{+21} & = & \color{red}{18x} +20 \\\Leftrightarrow & 168x \color{red}{+21} \color{blue}{-21} \color{blue}{-18x} & = & \color{red}{18x} +20 \color{blue}{-18x} \color{blue}{-21} \\\Leftrightarrow & 168x-18x& = & 20-21 \\\Leftrightarrow & \color{red}{150} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{150} & & \\ & V = \left\{ \frac{-1}{150} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{4}{5})& = & -8x+\frac{5}{4} \\\Leftrightarrow & -21x+\frac{28}{5}& = & -8x+\frac{5}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-420}{ \color{blue}{20} }x+ \frac{112}{ \color{blue}{20} })& = & (\frac{-160}{ \color{blue}{20} }x+ \frac{25}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -420x \color{red}{+112} & = & \color{red}{-160x} +25 \\\Leftrightarrow & -420x \color{red}{+112} \color{blue}{-112} \color{blue}{+160x} & = & \color{red}{-160x} +25 \color{blue}{+160x} \color{blue}{-112} \\\Leftrightarrow & -420x+160x& = & 25-112 \\\Leftrightarrow & \color{red}{-260} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-260} & & \\\Leftrightarrow & x = \frac{87}{260} & & \\ & V = \left\{ \frac{87}{260} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{7})& = & -3x+\frac{7}{10} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -3x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-560}{ \color{blue}{70} }x- \frac{60}{ \color{blue}{70} })& = & (\frac{-210}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -560x \color{red}{-60} & = & \color{red}{-210x} +49 \\\Leftrightarrow & -560x \color{red}{-60} \color{blue}{+60} \color{blue}{+210x} & = & \color{red}{-210x} +49 \color{blue}{+210x} \color{blue}{+60} \\\Leftrightarrow & -560x+210x& = & 49+60 \\\Leftrightarrow & \color{red}{-350} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-350} & & \\\Leftrightarrow & x = \frac{-109}{350} & & \\ & V = \left\{ \frac{-109}{350} \right\} & \\\end{align}\)