Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{2}{11})& = & -9x+\frac{3}{7} \\\Leftrightarrow & 16x+\frac{8}{11}& = & -9x+\frac{3}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{33}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+56} & = & \color{red}{-693x} +33 \\\Leftrightarrow & 1232x \color{red}{+56} \color{blue}{-56} \color{blue}{+693x} & = & \color{red}{-693x} +33 \color{blue}{+693x} \color{blue}{-56} \\\Leftrightarrow & 1232x+693x& = & 33-56 \\\Leftrightarrow & \color{red}{1925} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{1925} & & \\ & V = \left\{ \frac{-23}{1925} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x+\frac{4}{7})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{16}{7}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x- \frac{48}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{-48} & = & \color{red}{105x} +14 \\\Leftrightarrow & -252x \color{red}{-48} \color{blue}{+48} \color{blue}{-105x} & = & \color{red}{105x} +14 \color{blue}{-105x} \color{blue}{+48} \\\Leftrightarrow & -252x-105x& = & 14+48 \\\Leftrightarrow & \color{red}{-357} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-357} & & \\\Leftrightarrow & x = \frac{-62}{357} & & \\ & V = \left\{ \frac{-62}{357} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{2})& = & 3x+\frac{5}{11} \\\Leftrightarrow & 20x-\frac{25}{2}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{10}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-275} & = & \color{red}{66x} +10 \\\Leftrightarrow & 440x \color{red}{-275} \color{blue}{+275} \color{blue}{-66x} & = & \color{red}{66x} +10 \color{blue}{-66x} \color{blue}{+275} \\\Leftrightarrow & 440x-66x& = & 10+275 \\\Leftrightarrow & \color{red}{374} x& = & 285 \\\Leftrightarrow & x = \frac{285}{374} & & \\ & V = \left\{ \frac{285}{374} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{2}{9})& = & -6x+\frac{9}{2} \\\Leftrightarrow & -35x-\frac{14}{9}& = & -6x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-630}{ \color{blue}{18} }x- \frac{28}{ \color{blue}{18} })& = & (\frac{-108}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -630x \color{red}{-28} & = & \color{red}{-108x} +81 \\\Leftrightarrow & -630x \color{red}{-28} \color{blue}{+28} \color{blue}{+108x} & = & \color{red}{-108x} +81 \color{blue}{+108x} \color{blue}{+28} \\\Leftrightarrow & -630x+108x& = & 81+28 \\\Leftrightarrow & \color{red}{-522} x& = & 109 \\\Leftrightarrow & x = \frac{109}{-522} & & \\\Leftrightarrow & x = \frac{-109}{522} & & \\ & V = \left\{ \frac{-109}{522} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{6})& = & 2x+\frac{5}{2} \\\Leftrightarrow & 25x+\frac{25}{6}& = & 2x+\frac{5}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{150}{ \color{blue}{6} }x+ \frac{25}{ \color{blue}{6} })& = & (\frac{12}{ \color{blue}{6} }x+ \frac{15}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 150x \color{red}{+25} & = & \color{red}{12x} +15 \\\Leftrightarrow & 150x \color{red}{+25} \color{blue}{-25} \color{blue}{-12x} & = & \color{red}{12x} +15 \color{blue}{-12x} \color{blue}{-25} \\\Leftrightarrow & 150x-12x& = & 15-25 \\\Leftrightarrow & \color{red}{138} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{138} & & \\\Leftrightarrow & x = \frac{-5}{69} & & \\ & V = \left\{ \frac{-5}{69} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{9})& = & 8x+\frac{6}{11} \\\Leftrightarrow & -21x+\frac{35}{9}& = & 8x+\frac{6}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-2079}{ \color{blue}{99} }x+ \frac{385}{ \color{blue}{99} })& = & (\frac{792}{ \color{blue}{99} }x+ \frac{54}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -2079x \color{red}{+385} & = & \color{red}{792x} +54 \\\Leftrightarrow & -2079x \color{red}{+385} \color{blue}{-385} \color{blue}{-792x} & = & \color{red}{792x} +54 \color{blue}{-792x} \color{blue}{-385} \\\Leftrightarrow & -2079x-792x& = & 54-385 \\\Leftrightarrow & \color{red}{-2871} x& = & -331 \\\Leftrightarrow & x = \frac{-331}{-2871} & & \\\Leftrightarrow & x = \frac{331}{2871} & & \\ & V = \left\{ \frac{331}{2871} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{4}{7})& = & -7x+\frac{9}{2} \\\Leftrightarrow & 20x-\frac{16}{7}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{32}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-32} & = & \color{red}{-98x} +63 \\\Leftrightarrow & 280x \color{red}{-32} \color{blue}{+32} \color{blue}{+98x} & = & \color{red}{-98x} +63 \color{blue}{+98x} \color{blue}{+32} \\\Leftrightarrow & 280x+98x& = & 63+32 \\\Leftrightarrow & \color{red}{378} x& = & 95 \\\Leftrightarrow & x = \frac{95}{378} & & \\ & V = \left\{ \frac{95}{378} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{2}{11})& = & -7x+\frac{8}{3} \\\Leftrightarrow & 6x+\frac{4}{11}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+12} & = & \color{red}{-231x} +88 \\\Leftrightarrow & 198x \color{red}{+12} \color{blue}{-12} \color{blue}{+231x} & = & \color{red}{-231x} +88 \color{blue}{+231x} \color{blue}{-12} \\\Leftrightarrow & 198x+231x& = & 88-12 \\\Leftrightarrow & \color{red}{429} x& = & 76 \\\Leftrightarrow & x = \frac{76}{429} & & \\ & V = \left\{ \frac{76}{429} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & -9x+\frac{4}{7} \\\Leftrightarrow & -4x+\frac{10}{7}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-28}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{-63}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -28x \color{red}{+10} & = & \color{red}{-63x} +4 \\\Leftrightarrow & -28x \color{red}{+10} \color{blue}{-10} \color{blue}{+63x} & = & \color{red}{-63x} +4 \color{blue}{+63x} \color{blue}{-10} \\\Leftrightarrow & -28x+63x& = & 4-10 \\\Leftrightarrow & \color{red}{35} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{35} & & \\ & V = \left\{ \frac{-6}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{9})& = & -3x+\frac{2}{7} \\\Leftrightarrow & 10x-\frac{20}{9}& = & -3x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x- \frac{140}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{-140} & = & \color{red}{-189x} +18 \\\Leftrightarrow & 630x \color{red}{-140} \color{blue}{+140} \color{blue}{+189x} & = & \color{red}{-189x} +18 \color{blue}{+189x} \color{blue}{+140} \\\Leftrightarrow & 630x+189x& = & 18+140 \\\Leftrightarrow & \color{red}{819} x& = & 158 \\\Leftrightarrow & x = \frac{158}{819} & & \\ & V = \left\{ \frac{158}{819} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{2}{7})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-252}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -252x \color{red}{+18} & = & \color{red}{-105x} +56 \\\Leftrightarrow & -252x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +56 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & -252x+105x& = & 56-18 \\\Leftrightarrow & \color{red}{-147} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-147} & & \\\Leftrightarrow & x = \frac{-38}{147} & & \\ & V = \left\{ \frac{-38}{147} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{3}{5})& = & -9x+\frac{9}{5} \\\Leftrightarrow & 16x+\frac{12}{5}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{80}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 80x \color{red}{+12} & = & \color{red}{-45x} +9 \\\Leftrightarrow & 80x \color{red}{+12} \color{blue}{-12} \color{blue}{+45x} & = & \color{red}{-45x} +9 \color{blue}{+45x} \color{blue}{-12} \\\Leftrightarrow & 80x+45x& = & 9-12 \\\Leftrightarrow & \color{red}{125} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{125} & & \\ & V = \left\{ \frac{-3}{125} \right\} & \\\end{align}\)