Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{2})& = & -7x+\frac{6}{7} \\\Leftrightarrow & -10x-\frac{15}{2}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-140}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -140x \color{red}{-105} & = & \color{red}{-98x} +12 \\\Leftrightarrow & -140x \color{red}{-105} \color{blue}{+105} \color{blue}{+98x} & = & \color{red}{-98x} +12 \color{blue}{+98x} \color{blue}{+105} \\\Leftrightarrow & -140x+98x& = & 12+105 \\\Leftrightarrow & \color{red}{-42} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-42} & & \\\Leftrightarrow & x = \frac{-39}{14} & & \\ & V = \left\{ \frac{-39}{14} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{2}{5})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -8x+\frac{4}{5}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-40}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{45}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -40x \color{red}{+4} & = & \color{red}{45x} +8 \\\Leftrightarrow & -40x \color{red}{+4} \color{blue}{-4} \color{blue}{-45x} & = & \color{red}{45x} +8 \color{blue}{-45x} \color{blue}{-4} \\\Leftrightarrow & -40x-45x& = & 8-4 \\\Leftrightarrow & \color{red}{-85} x& = & 4 \\\Leftrightarrow & x = \frac{4}{-85} & & \\\Leftrightarrow & x = \frac{-4}{85} & & \\ & V = \left\{ \frac{-4}{85} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{2}{3})& = & -9x+\frac{9}{10} \\\Leftrightarrow & -35x-\frac{14}{3}& = & -9x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-1050}{ \color{blue}{30} }x- \frac{140}{ \color{blue}{30} })& = & (\frac{-270}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -1050x \color{red}{-140} & = & \color{red}{-270x} +27 \\\Leftrightarrow & -1050x \color{red}{-140} \color{blue}{+140} \color{blue}{+270x} & = & \color{red}{-270x} +27 \color{blue}{+270x} \color{blue}{+140} \\\Leftrightarrow & -1050x+270x& = & 27+140 \\\Leftrightarrow & \color{red}{-780} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-780} & & \\\Leftrightarrow & x = \frac{-167}{780} & & \\ & V = \left\{ \frac{-167}{780} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{3})& = & 5x+\frac{7}{3} \\\Leftrightarrow & 12x-\frac{16}{3}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x- \frac{16}{ \color{blue}{3} })& = & (\frac{15}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{-16} & = & \color{red}{15x} +7 \\\Leftrightarrow & 36x \color{red}{-16} \color{blue}{+16} \color{blue}{-15x} & = & \color{red}{15x} +7 \color{blue}{-15x} \color{blue}{+16} \\\Leftrightarrow & 36x-15x& = & 7+16 \\\Leftrightarrow & \color{red}{21} x& = & 23 \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{4}{7})& = & -3x+\frac{7}{11} \\\Leftrightarrow & 16x+\frac{16}{7}& = & -3x+\frac{7}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1232}{ \color{blue}{77} }x+ \frac{176}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{49}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1232x \color{red}{+176} & = & \color{red}{-231x} +49 \\\Leftrightarrow & 1232x \color{red}{+176} \color{blue}{-176} \color{blue}{+231x} & = & \color{red}{-231x} +49 \color{blue}{+231x} \color{blue}{-176} \\\Leftrightarrow & 1232x+231x& = & 49-176 \\\Leftrightarrow & \color{red}{1463} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{1463} & & \\ & V = \left\{ \frac{-127}{1463} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{2}{5})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 30x-\frac{12}{5}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{150}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{35}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 150x \color{red}{-12} & = & \color{red}{35x} +4 \\\Leftrightarrow & 150x \color{red}{-12} \color{blue}{+12} \color{blue}{-35x} & = & \color{red}{35x} +4 \color{blue}{-35x} \color{blue}{+12} \\\Leftrightarrow & 150x-35x& = & 4+12 \\\Leftrightarrow & \color{red}{115} x& = & 16 \\\Leftrightarrow & x = \frac{16}{115} & & \\ & V = \left\{ \frac{16}{115} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{3}{11})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 4x-\frac{6}{11}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{396}{ \color{blue}{99} }x- \frac{54}{ \color{blue}{99} })& = & (\frac{297}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 396x \color{red}{-54} & = & \color{red}{297x} +44 \\\Leftrightarrow & 396x \color{red}{-54} \color{blue}{+54} \color{blue}{-297x} & = & \color{red}{297x} +44 \color{blue}{-297x} \color{blue}{+54} \\\Leftrightarrow & 396x-297x& = & 44+54 \\\Leftrightarrow & \color{red}{99} x& = & 98 \\\Leftrightarrow & x = \frac{98}{99} & & \\ & V = \left\{ \frac{98}{99} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{2}{11})& = & 3x+\frac{2}{7} \\\Leftrightarrow & 14x+\frac{14}{11}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1078}{ \color{blue}{77} }x+ \frac{98}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1078x \color{red}{+98} & = & \color{red}{231x} +22 \\\Leftrightarrow & 1078x \color{red}{+98} \color{blue}{-98} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{-98} \\\Leftrightarrow & 1078x-231x& = & 22-98 \\\Leftrightarrow & \color{red}{847} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{847} & & \\ & V = \left\{ \frac{-76}{847} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x-\frac{2}{11})& = & -5x+\frac{4}{11} \\\Leftrightarrow & -9x-\frac{6}{11}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-99}{ \color{blue}{11} }x- \frac{6}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -99x \color{red}{-6} & = & \color{red}{-55x} +4 \\\Leftrightarrow & -99x \color{red}{-6} \color{blue}{+6} \color{blue}{+55x} & = & \color{red}{-55x} +4 \color{blue}{+55x} \color{blue}{+6} \\\Leftrightarrow & -99x+55x& = & 4+6 \\\Leftrightarrow & \color{red}{-44} x& = & 10 \\\Leftrightarrow & x = \frac{10}{-44} & & \\\Leftrightarrow & x = \frac{-5}{22} & & \\ & V = \left\{ \frac{-5}{22} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{11})& = & 4x+\frac{7}{4} \\\Leftrightarrow & -28x+\frac{35}{11}& = & 4x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-1232}{ \color{blue}{44} }x+ \frac{140}{ \color{blue}{44} })& = & (\frac{176}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -1232x \color{red}{+140} & = & \color{red}{176x} +77 \\\Leftrightarrow & -1232x \color{red}{+140} \color{blue}{-140} \color{blue}{-176x} & = & \color{red}{176x} +77 \color{blue}{-176x} \color{blue}{-140} \\\Leftrightarrow & -1232x-176x& = & 77-140 \\\Leftrightarrow & \color{red}{-1408} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{-1408} & & \\\Leftrightarrow & x = \frac{63}{1408} & & \\ & V = \left\{ \frac{63}{1408} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{7}{2} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{+24} & = & \color{red}{-50x} +35 \\\Leftrightarrow & 120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +35 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & 120x+50x& = & 35-24 \\\Leftrightarrow & \color{red}{170} x& = & 11 \\\Leftrightarrow & x = \frac{11}{170} & & \\ & V = \left\{ \frac{11}{170} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{3}{11})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 12x+\frac{18}{11}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{+126} & = & \color{red}{385x} +110 \\\Leftrightarrow & 924x \color{red}{+126} \color{blue}{-126} \color{blue}{-385x} & = & \color{red}{385x} +110 \color{blue}{-385x} \color{blue}{-126} \\\Leftrightarrow & 924x-385x& = & 110-126 \\\Leftrightarrow & \color{red}{539} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{539} & & \\ & V = \left\{ \frac{-16}{539} \right\} & \\\end{align}\)