Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{2}{7})& = & 4x+\frac{7}{10} \\\Leftrightarrow & -15x+\frac{6}{7}& = & 4x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-1050}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{280}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -1050x \color{red}{+60} & = & \color{red}{280x} +49 \\\Leftrightarrow & -1050x \color{red}{+60} \color{blue}{-60} \color{blue}{-280x} & = & \color{red}{280x} +49 \color{blue}{-280x} \color{blue}{-60} \\\Leftrightarrow & -1050x-280x& = & 49-60 \\\Leftrightarrow & \color{red}{-1330} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-1330} & & \\\Leftrightarrow & x = \frac{11}{1330} & & \\ & V = \left\{ \frac{11}{1330} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{5}{12})& = & -8x+\frac{3}{2} \\\Leftrightarrow & -21x-\frac{35}{12}& = & -8x+\frac{3}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{35}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{18}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-35} & = & \color{red}{-96x} +18 \\\Leftrightarrow & -252x \color{red}{-35} \color{blue}{+35} \color{blue}{+96x} & = & \color{red}{-96x} +18 \color{blue}{+96x} \color{blue}{+35} \\\Leftrightarrow & -252x+96x& = & 18+35 \\\Leftrightarrow & \color{red}{-156} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-156} & & \\\Leftrightarrow & x = \frac{-53}{156} & & \\ & V = \left\{ \frac{-53}{156} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x+\frac{4}{3})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -12x+\frac{16}{3}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{112}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+112} & = & \color{red}{105x} +6 \\\Leftrightarrow & -252x \color{red}{+112} \color{blue}{-112} \color{blue}{-105x} & = & \color{red}{105x} +6 \color{blue}{-105x} \color{blue}{-112} \\\Leftrightarrow & -252x-105x& = & 6-112 \\\Leftrightarrow & \color{red}{-357} x& = & -106 \\\Leftrightarrow & x = \frac{-106}{-357} & & \\\Leftrightarrow & x = \frac{106}{357} & & \\ & V = \left\{ \frac{106}{357} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{3}{8})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{704}{ \color{blue}{88} }x+ \frac{48}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{-231} & = & \color{red}{704x} +48 \\\Leftrightarrow & -1848x \color{red}{-231} \color{blue}{+231} \color{blue}{-704x} & = & \color{red}{704x} +48 \color{blue}{-704x} \color{blue}{+231} \\\Leftrightarrow & -1848x-704x& = & 48+231 \\\Leftrightarrow & \color{red}{-2552} x& = & 279 \\\Leftrightarrow & x = \frac{279}{-2552} & & \\\Leftrightarrow & x = \frac{-279}{2552} & & \\ & V = \left\{ \frac{-279}{2552} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{2}{3})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 21x-\frac{14}{3}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{693}{ \color{blue}{33} }x- \frac{154}{ \color{blue}{33} })& = & (\frac{66}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 693x \color{red}{-154} & = & \color{red}{66x} +6 \\\Leftrightarrow & 693x \color{red}{-154} \color{blue}{+154} \color{blue}{-66x} & = & \color{red}{66x} +6 \color{blue}{-66x} \color{blue}{+154} \\\Leftrightarrow & 693x-66x& = & 6+154 \\\Leftrightarrow & \color{red}{627} x& = & 160 \\\Leftrightarrow & x = \frac{160}{627} & & \\ & V = \left\{ \frac{160}{627} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{7})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 9x-\frac{9}{7}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{693}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 693x \color{red}{-99} & = & \color{red}{-539x} +28 \\\Leftrightarrow & 693x \color{red}{-99} \color{blue}{+99} \color{blue}{+539x} & = & \color{red}{-539x} +28 \color{blue}{+539x} \color{blue}{+99} \\\Leftrightarrow & 693x+539x& = & 28+99 \\\Leftrightarrow & \color{red}{1232} x& = & 127 \\\Leftrightarrow & x = \frac{127}{1232} & & \\ & V = \left\{ \frac{127}{1232} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -30x-\frac{18}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x- \frac{18}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{-18} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -150x \color{red}{-18} \color{blue}{+18} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{+18} \\\Leftrightarrow & -150x+35x& = & 6+18 \\\Leftrightarrow & \color{red}{-115} x& = & 24 \\\Leftrightarrow & x = \frac{24}{-115} & & \\\Leftrightarrow & x = \frac{-24}{115} & & \\ & V = \left\{ \frac{-24}{115} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{3})& = & -5x+\frac{2}{3} \\\Leftrightarrow & 14x-\frac{28}{3}& = & -5x+\frac{2}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{42}{ \color{blue}{3} }x- \frac{28}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{2}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 42x \color{red}{-28} & = & \color{red}{-15x} +2 \\\Leftrightarrow & 42x \color{red}{-28} \color{blue}{+28} \color{blue}{+15x} & = & \color{red}{-15x} +2 \color{blue}{+15x} \color{blue}{+28} \\\Leftrightarrow & 42x+15x& = & 2+28 \\\Leftrightarrow & \color{red}{57} x& = & 30 \\\Leftrightarrow & x = \frac{30}{57} & & \\\Leftrightarrow & x = \frac{10}{19} & & \\ & V = \left\{ \frac{10}{19} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{3}{5})& = & 5x+\frac{7}{11} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{35}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{-132} & = & \color{red}{275x} +35 \\\Leftrightarrow & -660x \color{red}{-132} \color{blue}{+132} \color{blue}{-275x} & = & \color{red}{275x} +35 \color{blue}{-275x} \color{blue}{+132} \\\Leftrightarrow & -660x-275x& = & 35+132 \\\Leftrightarrow & \color{red}{-935} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-935} & & \\\Leftrightarrow & x = \frac{-167}{935} & & \\ & V = \left\{ \frac{-167}{935} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{3}{7})& = & 5x+\frac{10}{7} \\\Leftrightarrow & -12x-\frac{9}{7}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-84}{ \color{blue}{7} }x- \frac{9}{ \color{blue}{7} })& = & (\frac{35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -84x \color{red}{-9} & = & \color{red}{35x} +10 \\\Leftrightarrow & -84x \color{red}{-9} \color{blue}{+9} \color{blue}{-35x} & = & \color{red}{35x} +10 \color{blue}{-35x} \color{blue}{+9} \\\Leftrightarrow & -84x-35x& = & 10+9 \\\Leftrightarrow & \color{red}{-119} x& = & 19 \\\Leftrightarrow & x = \frac{19}{-119} & & \\\Leftrightarrow & x = \frac{-19}{119} & & \\ & V = \left\{ \frac{-19}{119} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{5})& = & -5x+\frac{7}{3} \\\Leftrightarrow & -12x+\frac{24}{5}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-180}{ \color{blue}{15} }x+ \frac{72}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -180x \color{red}{+72} & = & \color{red}{-75x} +35 \\\Leftrightarrow & -180x \color{red}{+72} \color{blue}{-72} \color{blue}{+75x} & = & \color{red}{-75x} +35 \color{blue}{+75x} \color{blue}{-72} \\\Leftrightarrow & -180x+75x& = & 35-72 \\\Leftrightarrow & \color{red}{-105} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{-105} & & \\\Leftrightarrow & x = \frac{37}{105} & & \\ & V = \left\{ \frac{37}{105} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x-\frac{3}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & -16x-\frac{12}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-528}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -528x \color{red}{-36} & = & \color{red}{-231x} +22 \\\Leftrightarrow & -528x \color{red}{-36} \color{blue}{+36} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+36} \\\Leftrightarrow & -528x+231x& = & 22+36 \\\Leftrightarrow & \color{red}{-297} x& = & 58 \\\Leftrightarrow & x = \frac{58}{-297} & & \\\Leftrightarrow & x = \frac{-58}{297} & & \\ & V = \left\{ \frac{-58}{297} \right\} & \\\end{align}\)