Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{8})& = & 8x+\frac{10}{3} \\\Leftrightarrow & -21x-\frac{21}{8}& = & 8x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-504}{ \color{blue}{24} }x- \frac{63}{ \color{blue}{24} })& = & (\frac{192}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -504x \color{red}{-63} & = & \color{red}{192x} +80 \\\Leftrightarrow & -504x \color{red}{-63} \color{blue}{+63} \color{blue}{-192x} & = & \color{red}{192x} +80 \color{blue}{-192x} \color{blue}{+63} \\\Leftrightarrow & -504x-192x& = & 80+63 \\\Leftrightarrow & \color{red}{-696} x& = & 143 \\\Leftrightarrow & x = \frac{143}{-696} & & \\\Leftrightarrow & x = \frac{-143}{696} & & \\ & V = \left\{ \frac{-143}{696} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & 7x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{20}{7}& = & 7x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{20}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-20} & = & \color{red}{49x} +8 \\\Leftrightarrow & 84x \color{red}{-20} \color{blue}{+20} \color{blue}{-49x} & = & \color{red}{49x} +8 \color{blue}{-49x} \color{blue}{+20} \\\Leftrightarrow & 84x-49x& = & 8+20 \\\Leftrightarrow & \color{red}{35} x& = & 28 \\\Leftrightarrow & x = \frac{28}{35} & & \\\Leftrightarrow & x = \frac{4}{5} & & \\ & V = \left\{ \frac{4}{5} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{4}{7})& = & 5x+\frac{7}{3} \\\Leftrightarrow & -4x+\frac{8}{7}& = & 5x+\frac{7}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-84}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{49}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -84x \color{red}{+24} & = & \color{red}{105x} +49 \\\Leftrightarrow & -84x \color{red}{+24} \color{blue}{-24} \color{blue}{-105x} & = & \color{red}{105x} +49 \color{blue}{-105x} \color{blue}{-24} \\\Leftrightarrow & -84x-105x& = & 49-24 \\\Leftrightarrow & \color{red}{-189} x& = & 25 \\\Leftrightarrow & x = \frac{25}{-189} & & \\\Leftrightarrow & x = \frac{-25}{189} & & \\ & V = \left\{ \frac{-25}{189} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & 3x+\frac{3}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 3x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{105x} +21 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{-105x} & = & \color{red}{105x} +21 \color{blue}{-105x} \color{blue}{+150} \\\Leftrightarrow & -630x-105x& = & 21+150 \\\Leftrightarrow & \color{red}{-735} x& = & 171 \\\Leftrightarrow & x = \frac{171}{-735} & & \\\Leftrightarrow & x = \frac{-57}{245} & & \\ & V = \left\{ \frac{-57}{245} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{9})& = & 5x+\frac{3}{8} \\\Leftrightarrow & 14x+\frac{35}{9}& = & 5x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{1008}{ \color{blue}{72} }x+ \frac{280}{ \color{blue}{72} })& = & (\frac{360}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 1008x \color{red}{+280} & = & \color{red}{360x} +27 \\\Leftrightarrow & 1008x \color{red}{+280} \color{blue}{-280} \color{blue}{-360x} & = & \color{red}{360x} +27 \color{blue}{-360x} \color{blue}{-280} \\\Leftrightarrow & 1008x-360x& = & 27-280 \\\Leftrightarrow & \color{red}{648} x& = & -253 \\\Leftrightarrow & x = \frac{-253}{648} & & \\ & V = \left\{ \frac{-253}{648} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{4}{11})& = & 5x+\frac{9}{7} \\\Leftrightarrow & 18x+\frac{24}{11}& = & 5x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1386}{ \color{blue}{77} }x+ \frac{168}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1386x \color{red}{+168} & = & \color{red}{385x} +99 \\\Leftrightarrow & 1386x \color{red}{+168} \color{blue}{-168} \color{blue}{-385x} & = & \color{red}{385x} +99 \color{blue}{-385x} \color{blue}{-168} \\\Leftrightarrow & 1386x-385x& = & 99-168 \\\Leftrightarrow & \color{red}{1001} x& = & -69 \\\Leftrightarrow & x = \frac{-69}{1001} & & \\ & V = \left\{ \frac{-69}{1001} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x-\frac{3}{8})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -25x-\frac{15}{8}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-200}{ \color{blue}{8} }x- \frac{15}{ \color{blue}{8} })& = & (\frac{72}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -200x \color{red}{-15} & = & \color{red}{72x} +12 \\\Leftrightarrow & -200x \color{red}{-15} \color{blue}{+15} \color{blue}{-72x} & = & \color{red}{72x} +12 \color{blue}{-72x} \color{blue}{+15} \\\Leftrightarrow & -200x-72x& = & 12+15 \\\Leftrightarrow & \color{red}{-272} x& = & 27 \\\Leftrightarrow & x = \frac{27}{-272} & & \\\Leftrightarrow & x = \frac{-27}{272} & & \\ & V = \left\{ \frac{-27}{272} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{5}{6})& = & -3x+\frac{8}{3} \\\Leftrightarrow & 14x+\frac{35}{6}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 6 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{84}{ \color{blue}{6} }x+ \frac{35}{ \color{blue}{6} })& = & (\frac{-18}{ \color{blue}{6} }x+ \frac{16}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 84x \color{red}{+35} & = & \color{red}{-18x} +16 \\\Leftrightarrow & 84x \color{red}{+35} \color{blue}{-35} \color{blue}{+18x} & = & \color{red}{-18x} +16 \color{blue}{+18x} \color{blue}{-35} \\\Leftrightarrow & 84x+18x& = & 16-35 \\\Leftrightarrow & \color{red}{102} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{102} & & \\ & V = \left\{ \frac{-19}{102} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{4}{7})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{16}{7}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{16}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-16} & = & \color{red}{-35x} +10 \\\Leftrightarrow & 84x \color{red}{-16} \color{blue}{+16} \color{blue}{+35x} & = & \color{red}{-35x} +10 \color{blue}{+35x} \color{blue}{+16} \\\Leftrightarrow & 84x+35x& = & 10+16 \\\Leftrightarrow & \color{red}{119} x& = & 26 \\\Leftrightarrow & x = \frac{26}{119} & & \\ & V = \left\{ \frac{26}{119} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{11})& = & 7x+\frac{6}{11} \\\Leftrightarrow & -30x-\frac{24}{11}& = & 7x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-330}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -330x \color{red}{-24} & = & \color{red}{77x} +6 \\\Leftrightarrow & -330x \color{red}{-24} \color{blue}{+24} \color{blue}{-77x} & = & \color{red}{77x} +6 \color{blue}{-77x} \color{blue}{+24} \\\Leftrightarrow & -330x-77x& = & 6+24 \\\Leftrightarrow & \color{red}{-407} x& = & 30 \\\Leftrightarrow & x = \frac{30}{-407} & & \\\Leftrightarrow & x = \frac{-30}{407} & & \\ & V = \left\{ \frac{-30}{407} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{2}{5})& = & -5x+\frac{8}{9} \\\Leftrightarrow & -9x+\frac{6}{5}& = & -5x+\frac{8}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-405}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{40}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -405x \color{red}{+54} & = & \color{red}{-225x} +40 \\\Leftrightarrow & -405x \color{red}{+54} \color{blue}{-54} \color{blue}{+225x} & = & \color{red}{-225x} +40 \color{blue}{+225x} \color{blue}{-54} \\\Leftrightarrow & -405x+225x& = & 40-54 \\\Leftrightarrow & \color{red}{-180} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{-180} & & \\\Leftrightarrow & x = \frac{7}{90} & & \\ & V = \left\{ \frac{7}{90} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -10x+\frac{15}{8}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-560}{ \color{blue}{56} }x+ \frac{105}{ \color{blue}{56} })& = & (\frac{392}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -560x \color{red}{+105} & = & \color{red}{392x} +48 \\\Leftrightarrow & -560x \color{red}{+105} \color{blue}{-105} \color{blue}{-392x} & = & \color{red}{392x} +48 \color{blue}{-392x} \color{blue}{-105} \\\Leftrightarrow & -560x-392x& = & 48-105 \\\Leftrightarrow & \color{red}{-952} x& = & -57 \\\Leftrightarrow & x = \frac{-57}{-952} & & \\\Leftrightarrow & x = \frac{57}{952} & & \\ & V = \left\{ \frac{57}{952} \right\} & \\\end{align}\)