Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{3}{5})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -4x+\frac{6}{5}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+42} & = & \color{red}{315x} +10 \\\Leftrightarrow & -140x \color{red}{+42} \color{blue}{-42} \color{blue}{-315x} & = & \color{red}{315x} +10 \color{blue}{-315x} \color{blue}{-42} \\\Leftrightarrow & -140x-315x& = & 10-42 \\\Leftrightarrow & \color{red}{-455} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{-455} & & \\\Leftrightarrow & x = \frac{32}{455} & & \\ & V = \left\{ \frac{32}{455} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x+\frac{3}{7})& = & -7x+\frac{5}{7} \\\Leftrightarrow & -10x-\frac{6}{7}& = & -7x+\frac{5}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x- \frac{6}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{5}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{-6} & = & \color{red}{-49x} +5 \\\Leftrightarrow & -70x \color{red}{-6} \color{blue}{+6} \color{blue}{+49x} & = & \color{red}{-49x} +5 \color{blue}{+49x} \color{blue}{+6} \\\Leftrightarrow & -70x+49x& = & 5+6 \\\Leftrightarrow & \color{red}{-21} x& = & 11 \\\Leftrightarrow & x = \frac{11}{-21} & & \\\Leftrightarrow & x = \frac{-11}{21} & & \\ & V = \left\{ \frac{-11}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{4}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 16x+\frac{16}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{176}{ \color{blue}{11} }x+ \frac{16}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 176x \color{red}{+16} & = & \color{red}{-77x} +2 \\\Leftrightarrow & 176x \color{red}{+16} \color{blue}{-16} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-16} \\\Leftrightarrow & 176x+77x& = & 2-16 \\\Leftrightarrow & \color{red}{253} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{253} & & \\ & V = \left\{ \frac{-14}{253} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x-\frac{5}{7})& = & 5x+\frac{9}{11} \\\Leftrightarrow & -4x-\frac{10}{7}& = & 5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-110} & = & \color{red}{385x} +63 \\\Leftrightarrow & -308x \color{red}{-110} \color{blue}{+110} \color{blue}{-385x} & = & \color{red}{385x} +63 \color{blue}{-385x} \color{blue}{+110} \\\Leftrightarrow & -308x-385x& = & 63+110 \\\Leftrightarrow & \color{red}{-693} x& = & 173 \\\Leftrightarrow & x = \frac{173}{-693} & & \\\Leftrightarrow & x = \frac{-173}{693} & & \\ & V = \left\{ \frac{-173}{693} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{2}{5})& = & 7x+\frac{8}{7} \\\Leftrightarrow & -30x-\frac{12}{5}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{40}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-84} & = & \color{red}{245x} +40 \\\Leftrightarrow & -1050x \color{red}{-84} \color{blue}{+84} \color{blue}{-245x} & = & \color{red}{245x} +40 \color{blue}{-245x} \color{blue}{+84} \\\Leftrightarrow & -1050x-245x& = & 40+84 \\\Leftrightarrow & \color{red}{-1295} x& = & 124 \\\Leftrightarrow & x = \frac{124}{-1295} & & \\\Leftrightarrow & x = \frac{-124}{1295} & & \\ & V = \left\{ \frac{-124}{1295} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{5}{3})& = & 2x+\frac{6}{7} \\\Leftrightarrow & 21x+\frac{35}{3}& = & 2x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{441}{ \color{blue}{21} }x+ \frac{245}{ \color{blue}{21} })& = & (\frac{42}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 441x \color{red}{+245} & = & \color{red}{42x} +18 \\\Leftrightarrow & 441x \color{red}{+245} \color{blue}{-245} \color{blue}{-42x} & = & \color{red}{42x} +18 \color{blue}{-42x} \color{blue}{-245} \\\Leftrightarrow & 441x-42x& = & 18-245 \\\Leftrightarrow & \color{red}{399} x& = & -227 \\\Leftrightarrow & x = \frac{-227}{399} & & \\ & V = \left\{ \frac{-227}{399} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{2}{7})& = & -9x+\frac{8}{11} \\\Leftrightarrow & 10x+\frac{10}{7}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+110} & = & \color{red}{-693x} +56 \\\Leftrightarrow & 770x \color{red}{+110} \color{blue}{-110} \color{blue}{+693x} & = & \color{red}{-693x} +56 \color{blue}{+693x} \color{blue}{-110} \\\Leftrightarrow & 770x+693x& = & 56-110 \\\Leftrightarrow & \color{red}{1463} x& = & -54 \\\Leftrightarrow & x = \frac{-54}{1463} & & \\ & V = \left\{ \frac{-54}{1463} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x+\frac{4}{5})& = & -8x+\frac{10}{9} \\\Leftrightarrow & -15x-\frac{12}{5}& = & -8x+\frac{10}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-360}{ \color{blue}{45} }x+ \frac{50}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{-108} & = & \color{red}{-360x} +50 \\\Leftrightarrow & -675x \color{red}{-108} \color{blue}{+108} \color{blue}{+360x} & = & \color{red}{-360x} +50 \color{blue}{+360x} \color{blue}{+108} \\\Leftrightarrow & -675x+360x& = & 50+108 \\\Leftrightarrow & \color{red}{-315} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-315} & & \\\Leftrightarrow & x = \frac{-158}{315} & & \\ & V = \left\{ \frac{-158}{315} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{7})& = & 7x+\frac{10}{3} \\\Leftrightarrow & 25x+\frac{10}{7}& = & 7x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{147x} +70 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{-147x} & = & \color{red}{147x} +70 \color{blue}{-147x} \color{blue}{-30} \\\Leftrightarrow & 525x-147x& = & 70-30 \\\Leftrightarrow & \color{red}{378} x& = & 40 \\\Leftrightarrow & x = \frac{40}{378} & & \\\Leftrightarrow & x = \frac{20}{189} & & \\ & V = \left\{ \frac{20}{189} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{3}{8})& = & -9x+\frac{2}{7} \\\Leftrightarrow & 28x-\frac{21}{8}& = & -9x+\frac{2}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1568}{ \color{blue}{56} }x- \frac{147}{ \color{blue}{56} })& = & (\frac{-504}{ \color{blue}{56} }x+ \frac{16}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1568x \color{red}{-147} & = & \color{red}{-504x} +16 \\\Leftrightarrow & 1568x \color{red}{-147} \color{blue}{+147} \color{blue}{+504x} & = & \color{red}{-504x} +16 \color{blue}{+504x} \color{blue}{+147} \\\Leftrightarrow & 1568x+504x& = & 16+147 \\\Leftrightarrow & \color{red}{2072} x& = & 163 \\\Leftrightarrow & x = \frac{163}{2072} & & \\ & V = \left\{ \frac{163}{2072} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{4}{5})& = & 7x+\frac{9}{4} \\\Leftrightarrow & 30x+\frac{24}{5}& = & 7x+\frac{9}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{600}{ \color{blue}{20} }x+ \frac{96}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{45}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 600x \color{red}{+96} & = & \color{red}{140x} +45 \\\Leftrightarrow & 600x \color{red}{+96} \color{blue}{-96} \color{blue}{-140x} & = & \color{red}{140x} +45 \color{blue}{-140x} \color{blue}{-96} \\\Leftrightarrow & 600x-140x& = & 45-96 \\\Leftrightarrow & \color{red}{460} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{460} & & \\ & V = \left\{ \frac{-51}{460} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{5}{3})& = & -9x+\frac{6}{11} \\\Leftrightarrow & -28x-\frac{35}{3}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-924}{ \color{blue}{33} }x- \frac{385}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -924x \color{red}{-385} & = & \color{red}{-297x} +18 \\\Leftrightarrow & -924x \color{red}{-385} \color{blue}{+385} \color{blue}{+297x} & = & \color{red}{-297x} +18 \color{blue}{+297x} \color{blue}{+385} \\\Leftrightarrow & -924x+297x& = & 18+385 \\\Leftrightarrow & \color{red}{-627} x& = & 403 \\\Leftrightarrow & x = \frac{403}{-627} & & \\\Leftrightarrow & x = \frac{-403}{627} & & \\ & V = \left\{ \frac{-403}{627} \right\} & \\\end{align}\)