Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{2})& = & -2x+\frac{2}{7} \\\Leftrightarrow & 35x+\frac{35}{2}& = & -2x+\frac{2}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{490}{ \color{blue}{14} }x+ \frac{245}{ \color{blue}{14} })& = & (\frac{-28}{ \color{blue}{14} }x+ \frac{4}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 490x \color{red}{+245} & = & \color{red}{-28x} +4 \\\Leftrightarrow & 490x \color{red}{+245} \color{blue}{-245} \color{blue}{+28x} & = & \color{red}{-28x} +4 \color{blue}{+28x} \color{blue}{-245} \\\Leftrightarrow & 490x+28x& = & 4-245 \\\Leftrightarrow & \color{red}{518} x& = & -241 \\\Leftrightarrow & x = \frac{-241}{518} & & \\ & V = \left\{ \frac{-241}{518} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{5}{3})& = & 2x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{35}{3}& = & 2x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-84}{ \color{blue}{3} }x+ \frac{35}{ \color{blue}{3} })& = & (\frac{6}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -84x \color{red}{+35} & = & \color{red}{6x} +10 \\\Leftrightarrow & -84x \color{red}{+35} \color{blue}{-35} \color{blue}{-6x} & = & \color{red}{6x} +10 \color{blue}{-6x} \color{blue}{-35} \\\Leftrightarrow & -84x-6x& = & 10-35 \\\Leftrightarrow & \color{red}{-90} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{-90} & & \\\Leftrightarrow & x = \frac{5}{18} & & \\ & V = \left\{ \frac{5}{18} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & 7x+\frac{10}{9} \\\Leftrightarrow & 30x+\frac{30}{7}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{1890}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{441}{ \color{blue}{63} }x+ \frac{70}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 1890x \color{red}{+270} & = & \color{red}{441x} +70 \\\Leftrightarrow & 1890x \color{red}{+270} \color{blue}{-270} \color{blue}{-441x} & = & \color{red}{441x} +70 \color{blue}{-441x} \color{blue}{-270} \\\Leftrightarrow & 1890x-441x& = & 70-270 \\\Leftrightarrow & \color{red}{1449} x& = & -200 \\\Leftrightarrow & x = \frac{-200}{1449} & & \\ & V = \left\{ \frac{-200}{1449} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x-\frac{3}{8})& = & -3x+\frac{9}{10} \\\Leftrightarrow & -35x+\frac{21}{8}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 8 en 10 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1400}{ \color{blue}{40} }x+ \frac{105}{ \color{blue}{40} })& = & (\frac{-120}{ \color{blue}{40} }x+ \frac{36}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1400x \color{red}{+105} & = & \color{red}{-120x} +36 \\\Leftrightarrow & -1400x \color{red}{+105} \color{blue}{-105} \color{blue}{+120x} & = & \color{red}{-120x} +36 \color{blue}{+120x} \color{blue}{-105} \\\Leftrightarrow & -1400x+120x& = & 36-105 \\\Leftrightarrow & \color{red}{-1280} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{-1280} & & \\\Leftrightarrow & x = \frac{69}{1280} & & \\ & V = \left\{ \frac{69}{1280} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{2}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{12}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{84}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-84} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 924x \color{red}{-84} \color{blue}{+84} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{+84} \\\Leftrightarrow & 924x+385x& = & 110+84 \\\Leftrightarrow & \color{red}{1309} x& = & 194 \\\Leftrightarrow & x = \frac{194}{1309} & & \\ & V = \left\{ \frac{194}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{2}{3})& = & 9x+\frac{5}{9} \\\Leftrightarrow & 35x+\frac{14}{3}& = & 9x+\frac{5}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{315}{ \color{blue}{9} }x+ \frac{42}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 315x \color{red}{+42} & = & \color{red}{81x} +5 \\\Leftrightarrow & 315x \color{red}{+42} \color{blue}{-42} \color{blue}{-81x} & = & \color{red}{81x} +5 \color{blue}{-81x} \color{blue}{-42} \\\Leftrightarrow & 315x-81x& = & 5-42 \\\Leftrightarrow & \color{red}{234} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{234} & & \\ & V = \left\{ \frac{-37}{234} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{2})& = & 3x+\frac{8}{9} \\\Leftrightarrow & 14x+\frac{21}{2}& = & 3x+\frac{8}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{252}{ \color{blue}{18} }x+ \frac{189}{ \color{blue}{18} })& = & (\frac{54}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 252x \color{red}{+189} & = & \color{red}{54x} +16 \\\Leftrightarrow & 252x \color{red}{+189} \color{blue}{-189} \color{blue}{-54x} & = & \color{red}{54x} +16 \color{blue}{-54x} \color{blue}{-189} \\\Leftrightarrow & 252x-54x& = & 16-189 \\\Leftrightarrow & \color{red}{198} x& = & -173 \\\Leftrightarrow & x = \frac{-173}{198} & & \\ & V = \left\{ \frac{-173}{198} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{2}{11})& = & 7x+\frac{2}{5} \\\Leftrightarrow & 10x-\frac{10}{11}& = & 7x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{550}{ \color{blue}{55} }x- \frac{50}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 550x \color{red}{-50} & = & \color{red}{385x} +22 \\\Leftrightarrow & 550x \color{red}{-50} \color{blue}{+50} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{+50} \\\Leftrightarrow & 550x-385x& = & 22+50 \\\Leftrightarrow & \color{red}{165} x& = & 72 \\\Leftrightarrow & x = \frac{72}{165} & & \\\Leftrightarrow & x = \frac{24}{55} & & \\ & V = \left\{ \frac{24}{55} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (2x+\frac{3}{11})& = & -3x+\frac{2}{5} \\\Leftrightarrow & -14x-\frac{21}{11}& = & -3x+\frac{2}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-770}{ \color{blue}{55} }x- \frac{105}{ \color{blue}{55} })& = & (\frac{-165}{ \color{blue}{55} }x+ \frac{22}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -770x \color{red}{-105} & = & \color{red}{-165x} +22 \\\Leftrightarrow & -770x \color{red}{-105} \color{blue}{+105} \color{blue}{+165x} & = & \color{red}{-165x} +22 \color{blue}{+165x} \color{blue}{+105} \\\Leftrightarrow & -770x+165x& = & 22+105 \\\Leftrightarrow & \color{red}{-605} x& = & 127 \\\Leftrightarrow & x = \frac{127}{-605} & & \\\Leftrightarrow & x = \frac{-127}{605} & & \\ & V = \left\{ \frac{-127}{605} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{4}{3})& = & -7x+\frac{8}{7} \\\Leftrightarrow & -10x-\frac{8}{3}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-210}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -210x \color{red}{-56} & = & \color{red}{-147x} +24 \\\Leftrightarrow & -210x \color{red}{-56} \color{blue}{+56} \color{blue}{+147x} & = & \color{red}{-147x} +24 \color{blue}{+147x} \color{blue}{+56} \\\Leftrightarrow & -210x+147x& = & 24+56 \\\Leftrightarrow & \color{red}{-63} x& = & 80 \\\Leftrightarrow & x = \frac{80}{-63} & & \\\Leftrightarrow & x = \frac{-80}{63} & & \\ & V = \left\{ \frac{-80}{63} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{4}{3})& = & -5x+\frac{7}{9} \\\Leftrightarrow & 12x+\frac{16}{3}& = & -5x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{48}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+48} & = & \color{red}{-45x} +7 \\\Leftrightarrow & 108x \color{red}{+48} \color{blue}{-48} \color{blue}{+45x} & = & \color{red}{-45x} +7 \color{blue}{+45x} \color{blue}{-48} \\\Leftrightarrow & 108x+45x& = & 7-48 \\\Leftrightarrow & \color{red}{153} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{153} & & \\ & V = \left\{ \frac{-41}{153} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{2}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & -12x-\frac{8}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-108}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -108x \color{red}{-8} & = & \color{red}{45x} +6 \\\Leftrightarrow & -108x \color{red}{-8} \color{blue}{+8} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{+8} \\\Leftrightarrow & -108x-45x& = & 6+8 \\\Leftrightarrow & \color{red}{-153} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-153} & & \\\Leftrightarrow & x = \frac{-14}{153} & & \\ & V = \left\{ \frac{-14}{153} \right\} & \\\end{align}\)