Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{2}{9})& = & -5x+\frac{8}{7} \\\Leftrightarrow & 12x-\frac{8}{9}& = & -5x+\frac{8}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x- \frac{56}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{-56} & = & \color{red}{-315x} +72 \\\Leftrightarrow & 756x \color{red}{-56} \color{blue}{+56} \color{blue}{+315x} & = & \color{red}{-315x} +72 \color{blue}{+315x} \color{blue}{+56} \\\Leftrightarrow & 756x+315x& = & 72+56 \\\Leftrightarrow & \color{red}{1071} x& = & 128 \\\Leftrightarrow & x = \frac{128}{1071} & & \\ & V = \left\{ \frac{128}{1071} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{3}{5})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -20x-\frac{12}{5}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-400}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -400x \color{red}{-48} & = & \color{red}{-140x} +35 \\\Leftrightarrow & -400x \color{red}{-48} \color{blue}{+48} \color{blue}{+140x} & = & \color{red}{-140x} +35 \color{blue}{+140x} \color{blue}{+48} \\\Leftrightarrow & -400x+140x& = & 35+48 \\\Leftrightarrow & \color{red}{-260} x& = & 83 \\\Leftrightarrow & x = \frac{83}{-260} & & \\\Leftrightarrow & x = \frac{-83}{260} & & \\ & V = \left\{ \frac{-83}{260} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{4}{11})& = & -3x+\frac{3}{8} \\\Leftrightarrow & 8x+\frac{8}{11}& = & -3x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{704}{ \color{blue}{88} }x+ \frac{64}{ \color{blue}{88} })& = & (\frac{-264}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 704x \color{red}{+64} & = & \color{red}{-264x} +33 \\\Leftrightarrow & 704x \color{red}{+64} \color{blue}{-64} \color{blue}{+264x} & = & \color{red}{-264x} +33 \color{blue}{+264x} \color{blue}{-64} \\\Leftrightarrow & 704x+264x& = & 33-64 \\\Leftrightarrow & \color{red}{968} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{968} & & \\ & V = \left\{ \frac{-31}{968} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{8})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{15}{8}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-80}{ \color{blue}{8} }x+ \frac{15}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -80x \color{red}{+15} & = & \color{red}{-56x} +6 \\\Leftrightarrow & -80x \color{red}{+15} \color{blue}{-15} \color{blue}{+56x} & = & \color{red}{-56x} +6 \color{blue}{+56x} \color{blue}{-15} \\\Leftrightarrow & -80x+56x& = & 6-15 \\\Leftrightarrow & \color{red}{-24} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-24} & & \\\Leftrightarrow & x = \frac{3}{8} & & \\ & V = \left\{ \frac{3}{8} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{5}{7})& = & 7x+\frac{10}{11} \\\Leftrightarrow & -30x+\frac{30}{7}& = & 7x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+330} & = & \color{red}{539x} +70 \\\Leftrightarrow & -2310x \color{red}{+330} \color{blue}{-330} \color{blue}{-539x} & = & \color{red}{539x} +70 \color{blue}{-539x} \color{blue}{-330} \\\Leftrightarrow & -2310x-539x& = & 70-330 \\\Leftrightarrow & \color{red}{-2849} x& = & -260 \\\Leftrightarrow & x = \frac{-260}{-2849} & & \\\Leftrightarrow & x = \frac{260}{2849} & & \\ & V = \left\{ \frac{260}{2849} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{2}{11})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 25x+\frac{10}{11}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+30} & = & \color{red}{-66x} +22 \\\Leftrightarrow & 825x \color{red}{+30} \color{blue}{-30} \color{blue}{+66x} & = & \color{red}{-66x} +22 \color{blue}{+66x} \color{blue}{-30} \\\Leftrightarrow & 825x+66x& = & 22-30 \\\Leftrightarrow & \color{red}{891} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{891} & & \\ & V = \left\{ \frac{-8}{891} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{4}{7})& = & 2x+\frac{9}{5} \\\Leftrightarrow & 9x+\frac{12}{7}& = & 2x+\frac{9}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{63}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{+60} & = & \color{red}{70x} +63 \\\Leftrightarrow & 315x \color{red}{+60} \color{blue}{-60} \color{blue}{-70x} & = & \color{red}{70x} +63 \color{blue}{-70x} \color{blue}{-60} \\\Leftrightarrow & 315x-70x& = & 63-60 \\\Leftrightarrow & \color{red}{245} x& = & 3 \\\Leftrightarrow & x = \frac{3}{245} & & \\ & V = \left\{ \frac{3}{245} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x+\frac{4}{3})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 10x-\frac{20}{3}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{330}{ \color{blue}{33} }x- \frac{220}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 330x \color{red}{-220} & = & \color{red}{-231x} +6 \\\Leftrightarrow & 330x \color{red}{-220} \color{blue}{+220} \color{blue}{+231x} & = & \color{red}{-231x} +6 \color{blue}{+231x} \color{blue}{+220} \\\Leftrightarrow & 330x+231x& = & 6+220 \\\Leftrightarrow & \color{red}{561} x& = & 226 \\\Leftrightarrow & x = \frac{226}{561} & & \\ & V = \left\{ \frac{226}{561} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{2}{9})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -72x \color{red}{+8} & = & \color{red}{-81x} +6 \\\Leftrightarrow & -72x \color{red}{+8} \color{blue}{-8} \color{blue}{+81x} & = & \color{red}{-81x} +6 \color{blue}{+81x} \color{blue}{-8} \\\Leftrightarrow & -72x+81x& = & 6-8 \\\Leftrightarrow & \color{red}{9} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & 30x-\frac{30}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x- \frac{330}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{-330} & = & \color{red}{-539x} +35 \\\Leftrightarrow & 2310x \color{red}{-330} \color{blue}{+330} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{+330} \\\Leftrightarrow & 2310x+539x& = & 35+330 \\\Leftrightarrow & \color{red}{2849} x& = & 365 \\\Leftrightarrow & x = \frac{365}{2849} & & \\ & V = \left\{ \frac{365}{2849} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{5})& = & -7x+\frac{3}{5} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{3}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-150}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{3}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -150x \color{red}{+12} & = & \color{red}{-35x} +3 \\\Leftrightarrow & -150x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +3 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -150x+35x& = & 3-12 \\\Leftrightarrow & \color{red}{-115} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-115} & & \\\Leftrightarrow & x = \frac{9}{115} & & \\ & V = \left\{ \frac{9}{115} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{5})& = & -5x+\frac{4}{5} \\\Leftrightarrow & -9x-\frac{9}{5}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-45}{ \color{blue}{5} }x- \frac{9}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -45x \color{red}{-9} & = & \color{red}{-25x} +4 \\\Leftrightarrow & -45x \color{red}{-9} \color{blue}{+9} \color{blue}{+25x} & = & \color{red}{-25x} +4 \color{blue}{+25x} \color{blue}{+9} \\\Leftrightarrow & -45x+25x& = & 4+9 \\\Leftrightarrow & \color{red}{-20} x& = & 13 \\\Leftrightarrow & x = \frac{13}{-20} & & \\\Leftrightarrow & x = \frac{-13}{20} & & \\ & V = \left\{ \frac{-13}{20} \right\} & \\\end{align}\)