Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{5}{7})& = & -9x+\frac{8}{5} \\\Leftrightarrow & 4x+\frac{10}{7}& = & -9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{140}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 140x \color{red}{+50} & = & \color{red}{-315x} +56 \\\Leftrightarrow & 140x \color{red}{+50} \color{blue}{-50} \color{blue}{+315x} & = & \color{red}{-315x} +56 \color{blue}{+315x} \color{blue}{-50} \\\Leftrightarrow & 140x+315x& = & 56-50 \\\Leftrightarrow & \color{red}{455} x& = & 6 \\\Leftrightarrow & x = \frac{6}{455} & & \\ & V = \left\{ \frac{6}{455} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{3}{7})& = & 3x+\frac{4}{9} \\\Leftrightarrow & -8x-\frac{6}{7}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x- \frac{54}{ \color{blue}{63} })& = & (\frac{189}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{-54} & = & \color{red}{189x} +28 \\\Leftrightarrow & -504x \color{red}{-54} \color{blue}{+54} \color{blue}{-189x} & = & \color{red}{189x} +28 \color{blue}{-189x} \color{blue}{+54} \\\Leftrightarrow & -504x-189x& = & 28+54 \\\Leftrightarrow & \color{red}{-693} x& = & 82 \\\Leftrightarrow & x = \frac{82}{-693} & & \\\Leftrightarrow & x = \frac{-82}{693} & & \\ & V = \left\{ \frac{-82}{693} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{3}{11})& = & 5x+\frac{4}{3} \\\Leftrightarrow & 6x+\frac{6}{11}& = & 5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+18} & = & \color{red}{165x} +44 \\\Leftrightarrow & 198x \color{red}{+18} \color{blue}{-18} \color{blue}{-165x} & = & \color{red}{165x} +44 \color{blue}{-165x} \color{blue}{-18} \\\Leftrightarrow & 198x-165x& = & 44-18 \\\Leftrightarrow & \color{red}{33} x& = & 26 \\\Leftrightarrow & x = \frac{26}{33} & & \\ & V = \left\{ \frac{26}{33} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-144}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{60}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -144x \color{red}{-45} & = & \color{red}{60x} +8 \\\Leftrightarrow & -144x \color{red}{-45} \color{blue}{+45} \color{blue}{-60x} & = & \color{red}{60x} +8 \color{blue}{-60x} \color{blue}{+45} \\\Leftrightarrow & -144x-60x& = & 8+45 \\\Leftrightarrow & \color{red}{-204} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-204} & & \\\Leftrightarrow & x = \frac{-53}{204} & & \\ & V = \left\{ \frac{-53}{204} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x-\frac{3}{11})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 24x+\frac{18}{11}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 264x \color{red}{+18} & = & \color{red}{55x} +3 \\\Leftrightarrow & 264x \color{red}{+18} \color{blue}{-18} \color{blue}{-55x} & = & \color{red}{55x} +3 \color{blue}{-55x} \color{blue}{-18} \\\Leftrightarrow & 264x-55x& = & 3-18 \\\Leftrightarrow & \color{red}{209} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{209} & & \\ & V = \left\{ \frac{-15}{209} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{11})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 12x-\frac{16}{11}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{112}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-112} & = & \color{red}{-385x} +55 \\\Leftrightarrow & 924x \color{red}{-112} \color{blue}{+112} \color{blue}{+385x} & = & \color{red}{-385x} +55 \color{blue}{+385x} \color{blue}{+112} \\\Leftrightarrow & 924x+385x& = & 55+112 \\\Leftrightarrow & \color{red}{1309} x& = & 167 \\\Leftrightarrow & x = \frac{167}{1309} & & \\ & V = \left\{ \frac{167}{1309} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{3})& = & -2x+\frac{9}{10} \\\Leftrightarrow & 15x-\frac{25}{3}& = & -2x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{450}{ \color{blue}{30} }x- \frac{250}{ \color{blue}{30} })& = & (\frac{-60}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{-250} & = & \color{red}{-60x} +27 \\\Leftrightarrow & 450x \color{red}{-250} \color{blue}{+250} \color{blue}{+60x} & = & \color{red}{-60x} +27 \color{blue}{+60x} \color{blue}{+250} \\\Leftrightarrow & 450x+60x& = & 27+250 \\\Leftrightarrow & \color{red}{510} x& = & 277 \\\Leftrightarrow & x = \frac{277}{510} & & \\ & V = \left\{ \frac{277}{510} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-1)& = & 7x+\frac{2}{11} \\\Leftrightarrow & -10x+5& = & 7x+\frac{2}{11} \\ & & & \text{kgv van noemers 1 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-110}{ \color{blue}{11} }x+ \frac{55}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -110x \color{red}{+55} & = & \color{red}{77x} +2 \\\Leftrightarrow & -110x \color{red}{+55} \color{blue}{-55} \color{blue}{-77x} & = & \color{red}{77x} +2 \color{blue}{-77x} \color{blue}{-55} \\\Leftrightarrow & -110x-77x& = & 2-55 \\\Leftrightarrow & \color{red}{-187} x& = & -53 \\\Leftrightarrow & x = \frac{-53}{-187} & & \\\Leftrightarrow & x = \frac{53}{187} & & \\ & V = \left\{ \frac{53}{187} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{6}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{-18} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 297x \color{red}{-18} \color{blue}{+18} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+18} \\\Leftrightarrow & 297x+231x& = & 22+18 \\\Leftrightarrow & \color{red}{528} x& = & 40 \\\Leftrightarrow & x = \frac{40}{528} & & \\\Leftrightarrow & x = \frac{5}{66} & & \\ & V = \left\{ \frac{5}{66} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{2}{9})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 4x+\frac{4}{9}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{252}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 252x \color{red}{+28} & = & \color{red}{441x} +90 \\\Leftrightarrow & 252x \color{red}{+28} \color{blue}{-28} \color{blue}{-441x} & = & \color{red}{441x} +90 \color{blue}{-441x} \color{blue}{-28} \\\Leftrightarrow & 252x-441x& = & 90-28 \\\Leftrightarrow & \color{red}{-189} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-189} & & \\\Leftrightarrow & x = \frac{-62}{189} & & \\ & V = \left\{ \frac{-62}{189} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{2}{3})& = & 3x+\frac{2}{5} \\\Leftrightarrow & -14x-\frac{14}{3}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-210}{ \color{blue}{15} }x- \frac{70}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{6}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -210x \color{red}{-70} & = & \color{red}{45x} +6 \\\Leftrightarrow & -210x \color{red}{-70} \color{blue}{+70} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{+70} \\\Leftrightarrow & -210x-45x& = & 6+70 \\\Leftrightarrow & \color{red}{-255} x& = & 76 \\\Leftrightarrow & x = \frac{76}{-255} & & \\\Leftrightarrow & x = \frac{-76}{255} & & \\ & V = \left\{ \frac{-76}{255} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+2)& = & 8x+\frac{4}{7} \\\Leftrightarrow & 21x-14& = & 8x+\frac{4}{7} \\ & & & \text{kgv van noemers 1 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{147}{ \color{blue}{7} }x- \frac{98}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 147x \color{red}{-98} & = & \color{red}{56x} +4 \\\Leftrightarrow & 147x \color{red}{-98} \color{blue}{+98} \color{blue}{-56x} & = & \color{red}{56x} +4 \color{blue}{-56x} \color{blue}{+98} \\\Leftrightarrow & 147x-56x& = & 4+98 \\\Leftrightarrow & \color{red}{91} x& = & 102 \\\Leftrightarrow & x = \frac{102}{91} & & \\ & V = \left\{ \frac{102}{91} \right\} & \\\end{align}\)