Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{2}{5})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -6x+\frac{4}{5}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+4} & = & \color{red}{-35x} +6 \\\Leftrightarrow & -30x \color{red}{+4} \color{blue}{-4} \color{blue}{+35x} & = & \color{red}{-35x} +6 \color{blue}{+35x} \color{blue}{-4} \\\Leftrightarrow & -30x+35x& = & 6-4 \\\Leftrightarrow & \color{red}{5} x& = & 2 \\\Leftrightarrow & x = \frac{2}{5} & & \\ & V = \left\{ \frac{2}{5} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{5}{7})& = & -6x+\frac{10}{11} \\\Leftrightarrow & 25x-\frac{25}{7}& = & -6x+\frac{10}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{275}{ \color{blue}{77} })& = & (\frac{-462}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-275} & = & \color{red}{-462x} +70 \\\Leftrightarrow & 1925x \color{red}{-275} \color{blue}{+275} \color{blue}{+462x} & = & \color{red}{-462x} +70 \color{blue}{+462x} \color{blue}{+275} \\\Leftrightarrow & 1925x+462x& = & 70+275 \\\Leftrightarrow & \color{red}{2387} x& = & 345 \\\Leftrightarrow & x = \frac{345}{2387} & & \\ & V = \left\{ \frac{345}{2387} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x+\frac{2}{5})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 10x-\frac{4}{5}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{100}{ \color{blue}{10} }x- \frac{8}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{15}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 100x \color{red}{-8} & = & \color{red}{70x} +15 \\\Leftrightarrow & 100x \color{red}{-8} \color{blue}{+8} \color{blue}{-70x} & = & \color{red}{70x} +15 \color{blue}{-70x} \color{blue}{+8} \\\Leftrightarrow & 100x-70x& = & 15+8 \\\Leftrightarrow & \color{red}{30} x& = & 23 \\\Leftrightarrow & x = \frac{23}{30} & & \\ & V = \left\{ \frac{23}{30} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{5}{2})& = & 7x+\frac{6}{7} \\\Leftrightarrow & -6x+\frac{15}{2}& = & 7x+\frac{6}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x+ \frac{105}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{12}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{+105} & = & \color{red}{98x} +12 \\\Leftrightarrow & -84x \color{red}{+105} \color{blue}{-105} \color{blue}{-98x} & = & \color{red}{98x} +12 \color{blue}{-98x} \color{blue}{-105} \\\Leftrightarrow & -84x-98x& = & 12-105 \\\Leftrightarrow & \color{red}{-182} x& = & -93 \\\Leftrightarrow & x = \frac{-93}{-182} & & \\\Leftrightarrow & x = \frac{93}{182} & & \\ & V = \left\{ \frac{93}{182} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-\frac{1}{2})& = & -2x+\frac{5}{6} \\\Leftrightarrow & -28x+\frac{7}{2}& = & -2x+\frac{5}{6} \\ & & & \text{kgv van noemers 2 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{-168}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & -168x \color{red}{+21} & = & \color{red}{-12x} +5 \\\Leftrightarrow & -168x \color{red}{+21} \color{blue}{-21} \color{blue}{+12x} & = & \color{red}{-12x} +5 \color{blue}{+12x} \color{blue}{-21} \\\Leftrightarrow & -168x+12x& = & 5-21 \\\Leftrightarrow & \color{red}{-156} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-156} & & \\\Leftrightarrow & x = \frac{4}{39} & & \\ & V = \left\{ \frac{4}{39} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{3})& = & -5x+\frac{5}{3} \\\Leftrightarrow & 12x+\frac{8}{3}& = & -5x+\frac{5}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{-15x} +5 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{+15x} & = & \color{red}{-15x} +5 \color{blue}{+15x} \color{blue}{-8} \\\Leftrightarrow & 36x+15x& = & 5-8 \\\Leftrightarrow & \color{red}{51} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{51} & & \\\Leftrightarrow & x = \frac{-1}{17} & & \\ & V = \left\{ \frac{-1}{17} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{9})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -16x+\frac{8}{9}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 9 en 6 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-288}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} })& = & (\frac{-126}{ \color{blue}{18} }x+ \frac{21}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -288x \color{red}{+16} & = & \color{red}{-126x} +21 \\\Leftrightarrow & -288x \color{red}{+16} \color{blue}{-16} \color{blue}{+126x} & = & \color{red}{-126x} +21 \color{blue}{+126x} \color{blue}{-16} \\\Leftrightarrow & -288x+126x& = & 21-16 \\\Leftrightarrow & \color{red}{-162} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-162} & & \\\Leftrightarrow & x = \frac{-5}{162} & & \\ & V = \left\{ \frac{-5}{162} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{5}{3})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -6x-\frac{10}{3}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-180}{ \color{blue}{30} }x- \frac{100}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{21}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -180x \color{red}{-100} & = & \color{red}{-210x} +21 \\\Leftrightarrow & -180x \color{red}{-100} \color{blue}{+100} \color{blue}{+210x} & = & \color{red}{-210x} +21 \color{blue}{+210x} \color{blue}{+100} \\\Leftrightarrow & -180x+210x& = & 21+100 \\\Leftrightarrow & \color{red}{30} x& = & 121 \\\Leftrightarrow & x = \frac{121}{30} & & \\ & V = \left\{ \frac{121}{30} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{4}{3})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 15x-\frac{20}{3}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{90}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-12}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 90x \color{red}{-40} & = & \color{red}{-12x} +27 \\\Leftrightarrow & 90x \color{red}{-40} \color{blue}{+40} \color{blue}{+12x} & = & \color{red}{-12x} +27 \color{blue}{+12x} \color{blue}{+40} \\\Leftrightarrow & 90x+12x& = & 27+40 \\\Leftrightarrow & \color{red}{102} x& = & 67 \\\Leftrightarrow & x = \frac{67}{102} & & \\ & V = \left\{ \frac{67}{102} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{5}{11})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 30x-\frac{30}{11}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x- \frac{90}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{-90} & = & \color{red}{-231x} +22 \\\Leftrightarrow & 990x \color{red}{-90} \color{blue}{+90} \color{blue}{+231x} & = & \color{red}{-231x} +22 \color{blue}{+231x} \color{blue}{+90} \\\Leftrightarrow & 990x+231x& = & 22+90 \\\Leftrightarrow & \color{red}{1221} x& = & 112 \\\Leftrightarrow & x = \frac{112}{1221} & & \\ & V = \left\{ \frac{112}{1221} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{5}{11})& = & 7x+\frac{7}{10} \\\Leftrightarrow & -10x+\frac{10}{11}& = & 7x+\frac{7}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1100}{ \color{blue}{110} }x+ \frac{100}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{77}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1100x \color{red}{+100} & = & \color{red}{770x} +77 \\\Leftrightarrow & -1100x \color{red}{+100} \color{blue}{-100} \color{blue}{-770x} & = & \color{red}{770x} +77 \color{blue}{-770x} \color{blue}{-100} \\\Leftrightarrow & -1100x-770x& = & 77-100 \\\Leftrightarrow & \color{red}{-1870} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-1870} & & \\\Leftrightarrow & x = \frac{23}{1870} & & \\ & V = \left\{ \frac{23}{1870} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{5}{3})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -16x-\frac{20}{3}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 3 en 10 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x- \frac{200}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{-200} & = & \color{red}{210x} +27 \\\Leftrightarrow & -480x \color{red}{-200} \color{blue}{+200} \color{blue}{-210x} & = & \color{red}{210x} +27 \color{blue}{-210x} \color{blue}{+200} \\\Leftrightarrow & -480x-210x& = & 27+200 \\\Leftrightarrow & \color{red}{-690} x& = & 227 \\\Leftrightarrow & x = \frac{227}{-690} & & \\\Leftrightarrow & x = \frac{-227}{690} & & \\ & V = \left\{ \frac{-227}{690} \right\} & \\\end{align}\)