Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{4}{5})& = & 7x+\frac{4}{11} \\\Leftrightarrow & 24x-\frac{24}{5}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1320}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1320x \color{red}{-264} & = & \color{red}{385x} +20 \\\Leftrightarrow & 1320x \color{red}{-264} \color{blue}{+264} \color{blue}{-385x} & = & \color{red}{385x} +20 \color{blue}{-385x} \color{blue}{+264} \\\Leftrightarrow & 1320x-385x& = & 20+264 \\\Leftrightarrow & \color{red}{935} x& = & 284 \\\Leftrightarrow & x = \frac{284}{935} & & \\ & V = \left\{ \frac{284}{935} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{2}{5})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -10x-\frac{4}{5}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-550}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{30}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -550x \color{red}{-44} & = & \color{red}{-385x} +30 \\\Leftrightarrow & -550x \color{red}{-44} \color{blue}{+44} \color{blue}{+385x} & = & \color{red}{-385x} +30 \color{blue}{+385x} \color{blue}{+44} \\\Leftrightarrow & -550x+385x& = & 30+44 \\\Leftrightarrow & \color{red}{-165} x& = & 74 \\\Leftrightarrow & x = \frac{74}{-165} & & \\\Leftrightarrow & x = \frac{-74}{165} & & \\ & V = \left\{ \frac{-74}{165} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{11})& = & -7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{4}{11}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-770}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -770x \color{red}{+28} & = & \color{red}{-539x} +110 \\\Leftrightarrow & -770x \color{red}{+28} \color{blue}{-28} \color{blue}{+539x} & = & \color{red}{-539x} +110 \color{blue}{+539x} \color{blue}{-28} \\\Leftrightarrow & -770x+539x& = & 110-28 \\\Leftrightarrow & \color{red}{-231} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-231} & & \\\Leftrightarrow & x = \frac{-82}{231} & & \\ & V = \left\{ \frac{-82}{231} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{5}{11})& = & -5x+\frac{3}{11} \\\Leftrightarrow & 6x+\frac{10}{11}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{66}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 66x \color{red}{+10} & = & \color{red}{-55x} +3 \\\Leftrightarrow & 66x \color{red}{+10} \color{blue}{-10} \color{blue}{+55x} & = & \color{red}{-55x} +3 \color{blue}{+55x} \color{blue}{-10} \\\Leftrightarrow & 66x+55x& = & 3-10 \\\Leftrightarrow & \color{red}{121} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{121} & & \\ & V = \left\{ \frac{-7}{121} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{3}{7})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 6x-\frac{6}{7}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{18}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-18} & = & \color{red}{147x} +28 \\\Leftrightarrow & 126x \color{red}{-18} \color{blue}{+18} \color{blue}{-147x} & = & \color{red}{147x} +28 \color{blue}{-147x} \color{blue}{+18} \\\Leftrightarrow & 126x-147x& = & 28+18 \\\Leftrightarrow & \color{red}{-21} x& = & 46 \\\Leftrightarrow & x = \frac{46}{-21} & & \\\Leftrightarrow & x = \frac{-46}{21} & & \\ & V = \left\{ \frac{-46}{21} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x+\frac{3}{11})& = & -5x+\frac{5}{3} \\\Leftrightarrow & -12x-\frac{18}{11}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{55}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{-54} & = & \color{red}{-165x} +55 \\\Leftrightarrow & -396x \color{red}{-54} \color{blue}{+54} \color{blue}{+165x} & = & \color{red}{-165x} +55 \color{blue}{+165x} \color{blue}{+54} \\\Leftrightarrow & -396x+165x& = & 55+54 \\\Leftrightarrow & \color{red}{-231} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-231} & & \\\Leftrightarrow & x = \frac{-109}{231} & & \\ & V = \left\{ \frac{-109}{231} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{1050}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 1050x \color{red}{-150} & = & \color{red}{-245x} +42 \\\Leftrightarrow & 1050x \color{red}{-150} \color{blue}{+150} \color{blue}{+245x} & = & \color{red}{-245x} +42 \color{blue}{+245x} \color{blue}{+150} \\\Leftrightarrow & 1050x+245x& = & 42+150 \\\Leftrightarrow & \color{red}{1295} x& = & 192 \\\Leftrightarrow & x = \frac{192}{1295} & & \\ & V = \left\{ \frac{192}{1295} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{2}{11})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -30x-\frac{12}{11}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1320}{ \color{blue}{44} }x- \frac{48}{ \color{blue}{44} })& = & (\frac{308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1320x \color{red}{-48} & = & \color{red}{308x} +77 \\\Leftrightarrow & -1320x \color{red}{-48} \color{blue}{+48} \color{blue}{-308x} & = & \color{red}{308x} +77 \color{blue}{-308x} \color{blue}{+48} \\\Leftrightarrow & -1320x-308x& = & 77+48 \\\Leftrightarrow & \color{red}{-1628} x& = & 125 \\\Leftrightarrow & x = \frac{125}{-1628} & & \\\Leftrightarrow & x = \frac{-125}{1628} & & \\ & V = \left\{ \frac{-125}{1628} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+1)& = & 8x+\frac{3}{4} \\\Leftrightarrow & -21x-7& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-84}{ \color{blue}{4} }x- \frac{28}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -84x \color{red}{-28} & = & \color{red}{32x} +3 \\\Leftrightarrow & -84x \color{red}{-28} \color{blue}{+28} \color{blue}{-32x} & = & \color{red}{32x} +3 \color{blue}{-32x} \color{blue}{+28} \\\Leftrightarrow & -84x-32x& = & 3+28 \\\Leftrightarrow & \color{red}{-116} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-116} & & \\\Leftrightarrow & x = \frac{-31}{116} & & \\ & V = \left\{ \frac{-31}{116} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (4x-\frac{5}{7})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 24x-\frac{30}{7}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1512}{ \color{blue}{63} }x- \frac{270}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1512x \color{red}{-270} & = & \color{red}{-315x} +28 \\\Leftrightarrow & 1512x \color{red}{-270} \color{blue}{+270} \color{blue}{+315x} & = & \color{red}{-315x} +28 \color{blue}{+315x} \color{blue}{+270} \\\Leftrightarrow & 1512x+315x& = & 28+270 \\\Leftrightarrow & \color{red}{1827} x& = & 298 \\\Leftrightarrow & x = \frac{298}{1827} & & \\ & V = \left\{ \frac{298}{1827} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{4}{7})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -21x+4& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 1 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-42}{ \color{blue}{2} }x+ \frac{8}{ \color{blue}{2} })& = & (\frac{16}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -42x \color{red}{+8} & = & \color{red}{16x} +9 \\\Leftrightarrow & -42x \color{red}{+8} \color{blue}{-8} \color{blue}{-16x} & = & \color{red}{16x} +9 \color{blue}{-16x} \color{blue}{-8} \\\Leftrightarrow & -42x-16x& = & 9-8 \\\Leftrightarrow & \color{red}{-58} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-58} & & \\\Leftrightarrow & x = \frac{-1}{58} & & \\ & V = \left\{ \frac{-1}{58} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & -12x+\frac{6}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+42} & = & \color{red}{175x} +20 \\\Leftrightarrow & -420x \color{red}{+42} \color{blue}{-42} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{-42} \\\Leftrightarrow & -420x-175x& = & 20-42 \\\Leftrightarrow & \color{red}{-595} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{-595} & & \\\Leftrightarrow & x = \frac{22}{595} & & \\ & V = \left\{ \frac{22}{595} \right\} & \\\end{align}\)