Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{4})& = & -6x+\frac{5}{2} \\\Leftrightarrow & 25x-\frac{25}{4}& = & -6x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x- \frac{25}{ \color{blue}{4} })& = & (\frac{-24}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{-25} & = & \color{red}{-24x} +10 \\\Leftrightarrow & 100x \color{red}{-25} \color{blue}{+25} \color{blue}{+24x} & = & \color{red}{-24x} +10 \color{blue}{+24x} \color{blue}{+25} \\\Leftrightarrow & 100x+24x& = & 10+25 \\\Leftrightarrow & \color{red}{124} x& = & 35 \\\Leftrightarrow & x = \frac{35}{124} & & \\ & V = \left\{ \frac{35}{124} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{5})& = & -6x+\frac{8}{5} \\\Leftrightarrow & 35x+\frac{14}{5}& = & -6x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{175}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-30}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 175x \color{red}{+14} & = & \color{red}{-30x} +8 \\\Leftrightarrow & 175x \color{red}{+14} \color{blue}{-14} \color{blue}{+30x} & = & \color{red}{-30x} +8 \color{blue}{+30x} \color{blue}{-14} \\\Leftrightarrow & 175x+30x& = & 8-14 \\\Leftrightarrow & \color{red}{205} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{205} & & \\ & V = \left\{ \frac{-6}{205} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x-\frac{5}{7})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{15}{7}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-756}{ \color{blue}{63} }x- \frac{135}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -756x \color{red}{-135} & = & \color{red}{315x} +56 \\\Leftrightarrow & -756x \color{red}{-135} \color{blue}{+135} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{+135} \\\Leftrightarrow & -756x-315x& = & 56+135 \\\Leftrightarrow & \color{red}{-1071} x& = & 191 \\\Leftrightarrow & x = \frac{191}{-1071} & & \\\Leftrightarrow & x = \frac{-191}{1071} & & \\ & V = \left\{ \frac{-191}{1071} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & 5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{12}{5}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 120x \color{red}{-24} & = & \color{red}{50x} +45 \\\Leftrightarrow & 120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +45 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & 120x-50x& = & 45+24 \\\Leftrightarrow & \color{red}{70} x& = & 69 \\\Leftrightarrow & x = \frac{69}{70} & & \\ & V = \left\{ \frac{69}{70} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{2}{9})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -4x+\frac{4}{9}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-36}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -36x \color{red}{+4} & = & \color{red}{45x} +30 \\\Leftrightarrow & -36x \color{red}{+4} \color{blue}{-4} \color{blue}{-45x} & = & \color{red}{45x} +30 \color{blue}{-45x} \color{blue}{-4} \\\Leftrightarrow & -36x-45x& = & 30-4 \\\Leftrightarrow & \color{red}{-81} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-81} & & \\\Leftrightarrow & x = \frac{-26}{81} & & \\ & V = \left\{ \frac{-26}{81} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{5}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{+90} & = & \color{red}{147x} +70 \\\Leftrightarrow & 630x \color{red}{+90} \color{blue}{-90} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-90} \\\Leftrightarrow & 630x-147x& = & 70-90 \\\Leftrightarrow & \color{red}{483} x& = & -20 \\\Leftrightarrow & x = \frac{-20}{483} & & \\ & V = \left\{ \frac{-20}{483} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{5}{11})& = & 3x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{10}{11}& = & 3x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-176}{ \color{blue}{22} }x+ \frac{20}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -176x \color{red}{+20} & = & \color{red}{66x} +99 \\\Leftrightarrow & -176x \color{red}{+20} \color{blue}{-20} \color{blue}{-66x} & = & \color{red}{66x} +99 \color{blue}{-66x} \color{blue}{-20} \\\Leftrightarrow & -176x-66x& = & 99-20 \\\Leftrightarrow & \color{red}{-242} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-242} & & \\\Leftrightarrow & x = \frac{-79}{242} & & \\ & V = \left\{ \frac{-79}{242} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{11})& = & 5x+\frac{7}{11} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{7}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{198}{ \color{blue}{11} }x- \frac{18}{ \color{blue}{11} })& = & (\frac{55}{ \color{blue}{11} }x+ \frac{7}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 198x \color{red}{-18} & = & \color{red}{55x} +7 \\\Leftrightarrow & 198x \color{red}{-18} \color{blue}{+18} \color{blue}{-55x} & = & \color{red}{55x} +7 \color{blue}{-55x} \color{blue}{+18} \\\Leftrightarrow & 198x-55x& = & 7+18 \\\Leftrightarrow & \color{red}{143} x& = & 25 \\\Leftrightarrow & x = \frac{25}{143} & & \\ & V = \left\{ \frac{25}{143} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-50x} +25 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -120x+50x& = & 25-24 \\\Leftrightarrow & \color{red}{-70} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-70} & & \\\Leftrightarrow & x = \frac{-1}{70} & & \\ & V = \left\{ \frac{-1}{70} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{5}{2})& = & 5x+\frac{3}{7} \\\Leftrightarrow & 12x-\frac{15}{2}& = & 5x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{105}{ \color{blue}{14} })& = & (\frac{70}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-105} & = & \color{red}{70x} +6 \\\Leftrightarrow & 168x \color{red}{-105} \color{blue}{+105} \color{blue}{-70x} & = & \color{red}{70x} +6 \color{blue}{-70x} \color{blue}{+105} \\\Leftrightarrow & 168x-70x& = & 6+105 \\\Leftrightarrow & \color{red}{98} x& = & 111 \\\Leftrightarrow & x = \frac{111}{98} & & \\ & V = \left\{ \frac{111}{98} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{10})& = & 8x+\frac{2}{5} \\\Leftrightarrow & -15x+\frac{9}{10}& = & 8x+\frac{2}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{80}{ \color{blue}{10} }x+ \frac{4}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{+9} & = & \color{red}{80x} +4 \\\Leftrightarrow & -150x \color{red}{+9} \color{blue}{-9} \color{blue}{-80x} & = & \color{red}{80x} +4 \color{blue}{-80x} \color{blue}{-9} \\\Leftrightarrow & -150x-80x& = & 4-9 \\\Leftrightarrow & \color{red}{-230} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-230} & & \\\Leftrightarrow & x = \frac{1}{46} & & \\ & V = \left\{ \frac{1}{46} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -16x+\frac{16}{7}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-336}{ \color{blue}{21} }x+ \frac{48}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -336x \color{red}{+48} & = & \color{red}{-147x} +56 \\\Leftrightarrow & -336x \color{red}{+48} \color{blue}{-48} \color{blue}{+147x} & = & \color{red}{-147x} +56 \color{blue}{+147x} \color{blue}{-48} \\\Leftrightarrow & -336x+147x& = & 56-48 \\\Leftrightarrow & \color{red}{-189} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-189} & & \\\Leftrightarrow & x = \frac{-8}{189} & & \\ & V = \left\{ \frac{-8}{189} \right\} & \\\end{align}\)