Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{5}{7})& = & 5x+\frac{7}{6} \\\Leftrightarrow & -24x-\frac{30}{7}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-1008}{ \color{blue}{42} }x- \frac{180}{ \color{blue}{42} })& = & (\frac{210}{ \color{blue}{42} }x+ \frac{49}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -1008x \color{red}{-180} & = & \color{red}{210x} +49 \\\Leftrightarrow & -1008x \color{red}{-180} \color{blue}{+180} \color{blue}{-210x} & = & \color{red}{210x} +49 \color{blue}{-210x} \color{blue}{+180} \\\Leftrightarrow & -1008x-210x& = & 49+180 \\\Leftrightarrow & \color{red}{-1218} x& = & 229 \\\Leftrightarrow & x = \frac{229}{-1218} & & \\\Leftrightarrow & x = \frac{-229}{1218} & & \\ & V = \left\{ \frac{-229}{1218} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{5}{7})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -30x+\frac{30}{7}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-2310}{ \color{blue}{77} }x+ \frac{330}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -2310x \color{red}{+330} & = & \color{red}{-539x} +35 \\\Leftrightarrow & -2310x \color{red}{+330} \color{blue}{-330} \color{blue}{+539x} & = & \color{red}{-539x} +35 \color{blue}{+539x} \color{blue}{-330} \\\Leftrightarrow & -2310x+539x& = & 35-330 \\\Leftrightarrow & \color{red}{-1771} x& = & -295 \\\Leftrightarrow & x = \frac{-295}{-1771} & & \\\Leftrightarrow & x = \frac{295}{1771} & & \\ & V = \left\{ \frac{295}{1771} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{3}{8})& = & -8x+\frac{9}{11} \\\Leftrightarrow & -21x-\frac{21}{8}& = & -8x+\frac{9}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-1848}{ \color{blue}{88} }x- \frac{231}{ \color{blue}{88} })& = & (\frac{-704}{ \color{blue}{88} }x+ \frac{72}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -1848x \color{red}{-231} & = & \color{red}{-704x} +72 \\\Leftrightarrow & -1848x \color{red}{-231} \color{blue}{+231} \color{blue}{+704x} & = & \color{red}{-704x} +72 \color{blue}{+704x} \color{blue}{+231} \\\Leftrightarrow & -1848x+704x& = & 72+231 \\\Leftrightarrow & \color{red}{-1144} x& = & 303 \\\Leftrightarrow & x = \frac{303}{-1144} & & \\\Leftrightarrow & x = \frac{-303}{1144} & & \\ & V = \left\{ \frac{-303}{1144} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{1}{2})& = & -3x+\frac{9}{4} \\\Leftrightarrow & 10x+\frac{5}{2}& = & -3x+\frac{9}{4} \\ & & & \text{kgv van noemers 2 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{40}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} })& = & (\frac{-12}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 40x \color{red}{+10} & = & \color{red}{-12x} +9 \\\Leftrightarrow & 40x \color{red}{+10} \color{blue}{-10} \color{blue}{+12x} & = & \color{red}{-12x} +9 \color{blue}{+12x} \color{blue}{-10} \\\Leftrightarrow & 40x+12x& = & 9-10 \\\Leftrightarrow & \color{red}{52} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{52} & & \\ & V = \left\{ \frac{-1}{52} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{12}{5}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{70}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{-84} & = & \color{red}{70x} +50 \\\Leftrightarrow & 525x \color{red}{-84} \color{blue}{+84} \color{blue}{-70x} & = & \color{red}{70x} +50 \color{blue}{-70x} \color{blue}{+84} \\\Leftrightarrow & 525x-70x& = & 50+84 \\\Leftrightarrow & \color{red}{455} x& = & 134 \\\Leftrightarrow & x = \frac{134}{455} & & \\ & V = \left\{ \frac{134}{455} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{6}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+66} & = & \color{red}{275x} +10 \\\Leftrightarrow & -660x \color{red}{+66} \color{blue}{-66} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{-66} \\\Leftrightarrow & -660x-275x& = & 10-66 \\\Leftrightarrow & \color{red}{-935} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{-935} & & \\\Leftrightarrow & x = \frac{56}{935} & & \\ & V = \left\{ \frac{56}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{2}{9})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 9 en 2 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-288}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{81}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -288x \color{red}{+16} & = & \color{red}{-126x} +81 \\\Leftrightarrow & -288x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +81 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & -288x+126x& = & 81-16 \\\Leftrightarrow & \color{red}{-162} x& = & 65 \\\Leftrightarrow & x = \frac{65}{-162} & & \\\Leftrightarrow & x = \frac{-65}{162} & & \\ & V = \left\{ \frac{-65}{162} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x-\frac{2}{3})& = & 2x+\frac{9}{10} \\\Leftrightarrow & 21x+\frac{14}{3}& = & 2x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{630}{ \color{blue}{30} }x+ \frac{140}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 630x \color{red}{+140} & = & \color{red}{60x} +27 \\\Leftrightarrow & 630x \color{red}{+140} \color{blue}{-140} \color{blue}{-60x} & = & \color{red}{60x} +27 \color{blue}{-60x} \color{blue}{-140} \\\Leftrightarrow & 630x-60x& = & 27-140 \\\Leftrightarrow & \color{red}{570} x& = & -113 \\\Leftrightarrow & x = \frac{-113}{570} & & \\ & V = \left\{ \frac{-113}{570} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{5}{9})& = & 5x+\frac{2}{3} \\\Leftrightarrow & 12x+\frac{20}{9}& = & 5x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{108}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 108x \color{red}{+20} & = & \color{red}{45x} +6 \\\Leftrightarrow & 108x \color{red}{+20} \color{blue}{-20} \color{blue}{-45x} & = & \color{red}{45x} +6 \color{blue}{-45x} \color{blue}{-20} \\\Leftrightarrow & 108x-45x& = & 6-20 \\\Leftrightarrow & \color{red}{63} x& = & -14 \\\Leftrightarrow & x = \frac{-14}{63} & & \\\Leftrightarrow & x = \frac{-2}{9} & & \\ & V = \left\{ \frac{-2}{9} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x-\frac{2}{9})& = & 3x+\frac{7}{9} \\\Leftrightarrow & 20x+\frac{8}{9}& = & 3x+\frac{7}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{180}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 180x \color{red}{+8} & = & \color{red}{27x} +7 \\\Leftrightarrow & 180x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +7 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & 180x-27x& = & 7-8 \\\Leftrightarrow & \color{red}{153} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{153} & & \\ & V = \left\{ \frac{-1}{153} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x-\frac{4}{3})& = & -5x+\frac{7}{5} \\\Leftrightarrow & 16x-\frac{16}{3}& = & -5x+\frac{7}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{240}{ \color{blue}{15} }x- \frac{80}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{21}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 240x \color{red}{-80} & = & \color{red}{-75x} +21 \\\Leftrightarrow & 240x \color{red}{-80} \color{blue}{+80} \color{blue}{+75x} & = & \color{red}{-75x} +21 \color{blue}{+75x} \color{blue}{+80} \\\Leftrightarrow & 240x+75x& = & 21+80 \\\Leftrightarrow & \color{red}{315} x& = & 101 \\\Leftrightarrow & x = \frac{101}{315} & & \\ & V = \left\{ \frac{101}{315} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{3}{5})& = & -9x+\frac{2}{3} \\\Leftrightarrow & -8x-\frac{12}{5}& = & -9x+\frac{2}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-120}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-135}{ \color{blue}{15} }x+ \frac{10}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -120x \color{red}{-36} & = & \color{red}{-135x} +10 \\\Leftrightarrow & -120x \color{red}{-36} \color{blue}{+36} \color{blue}{+135x} & = & \color{red}{-135x} +10 \color{blue}{+135x} \color{blue}{+36} \\\Leftrightarrow & -120x+135x& = & 10+36 \\\Leftrightarrow & \color{red}{15} x& = & 46 \\\Leftrightarrow & x = \frac{46}{15} & & \\ & V = \left\{ \frac{46}{15} \right\} & \\\end{align}\)