Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{4}{3})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 8x+\frac{8}{3}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{18}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{+40} & = & \color{red}{-105x} +18 \\\Leftrightarrow & 120x \color{red}{+40} \color{blue}{-40} \color{blue}{+105x} & = & \color{red}{-105x} +18 \color{blue}{+105x} \color{blue}{-40} \\\Leftrightarrow & 120x+105x& = & 18-40 \\\Leftrightarrow & \color{red}{225} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{225} & & \\ & V = \left\{ \frac{-22}{225} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{3}{10})& = & -5x+\frac{5}{6} \\\Leftrightarrow & -12x+\frac{9}{10}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 10 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-360}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{-150}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -360x \color{red}{+27} & = & \color{red}{-150x} +25 \\\Leftrightarrow & -360x \color{red}{+27} \color{blue}{-27} \color{blue}{+150x} & = & \color{red}{-150x} +25 \color{blue}{+150x} \color{blue}{-27} \\\Leftrightarrow & -360x+150x& = & 25-27 \\\Leftrightarrow & \color{red}{-210} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-210} & & \\\Leftrightarrow & x = \frac{1}{105} & & \\ & V = \left\{ \frac{1}{105} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{4}{11})& = & -4x+\frac{8}{7} \\\Leftrightarrow & -25x+\frac{20}{11}& = & -4x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{-308}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{+140} & = & \color{red}{-308x} +88 \\\Leftrightarrow & -1925x \color{red}{+140} \color{blue}{-140} \color{blue}{+308x} & = & \color{red}{-308x} +88 \color{blue}{+308x} \color{blue}{-140} \\\Leftrightarrow & -1925x+308x& = & 88-140 \\\Leftrightarrow & \color{red}{-1617} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{-1617} & & \\\Leftrightarrow & x = \frac{52}{1617} & & \\ & V = \left\{ \frac{52}{1617} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x-\frac{4}{5})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 6x+\frac{12}{5}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 30x \color{red}{+12} & = & \color{red}{-25x} +6 \\\Leftrightarrow & 30x \color{red}{+12} \color{blue}{-12} \color{blue}{+25x} & = & \color{red}{-25x} +6 \color{blue}{+25x} \color{blue}{-12} \\\Leftrightarrow & 30x+25x& = & 6-12 \\\Leftrightarrow & \color{red}{55} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{55} & & \\ & V = \left\{ \frac{-6}{55} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{5}{6})& = & -2x+\frac{3}{5} \\\Leftrightarrow & 15x-\frac{25}{6}& = & -2x+\frac{3}{5} \\ & & & \text{kgv van noemers 6 en 5 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{450}{ \color{blue}{30} }x- \frac{125}{ \color{blue}{30} })& = & (\frac{-60}{ \color{blue}{30} }x+ \frac{18}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{-125} & = & \color{red}{-60x} +18 \\\Leftrightarrow & 450x \color{red}{-125} \color{blue}{+125} \color{blue}{+60x} & = & \color{red}{-60x} +18 \color{blue}{+60x} \color{blue}{+125} \\\Leftrightarrow & 450x+60x& = & 18+125 \\\Leftrightarrow & \color{red}{510} x& = & 143 \\\Leftrightarrow & x = \frac{143}{510} & & \\ & V = \left\{ \frac{143}{510} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{11})& = & 3x+\frac{4}{7} \\\Leftrightarrow & -18x-\frac{30}{11}& = & 3x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1386}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1386x \color{red}{-210} & = & \color{red}{231x} +44 \\\Leftrightarrow & -1386x \color{red}{-210} \color{blue}{+210} \color{blue}{-231x} & = & \color{red}{231x} +44 \color{blue}{-231x} \color{blue}{+210} \\\Leftrightarrow & -1386x-231x& = & 44+210 \\\Leftrightarrow & \color{red}{-1617} x& = & 254 \\\Leftrightarrow & x = \frac{254}{-1617} & & \\\Leftrightarrow & x = \frac{-254}{1617} & & \\ & V = \left\{ \frac{-254}{1617} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{3}{11})& = & 7x+\frac{8}{3} \\\Leftrightarrow & 30x+\frac{18}{11}& = & 7x+\frac{8}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{990}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 990x \color{red}{+54} & = & \color{red}{231x} +88 \\\Leftrightarrow & 990x \color{red}{+54} \color{blue}{-54} \color{blue}{-231x} & = & \color{red}{231x} +88 \color{blue}{-231x} \color{blue}{-54} \\\Leftrightarrow & 990x-231x& = & 88-54 \\\Leftrightarrow & \color{red}{759} x& = & 34 \\\Leftrightarrow & x = \frac{34}{759} & & \\ & V = \left\{ \frac{34}{759} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{4}{9})& = & -9x+\frac{3}{8} \\\Leftrightarrow & -8x+\frac{8}{9}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-576}{ \color{blue}{72} }x+ \frac{64}{ \color{blue}{72} })& = & (\frac{-648}{ \color{blue}{72} }x+ \frac{27}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -576x \color{red}{+64} & = & \color{red}{-648x} +27 \\\Leftrightarrow & -576x \color{red}{+64} \color{blue}{-64} \color{blue}{+648x} & = & \color{red}{-648x} +27 \color{blue}{+648x} \color{blue}{-64} \\\Leftrightarrow & -576x+648x& = & 27-64 \\\Leftrightarrow & \color{red}{72} x& = & -37 \\\Leftrightarrow & x = \frac{-37}{72} & & \\ & V = \left\{ \frac{-37}{72} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{7})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 12x-\frac{30}{7}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{63}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{-60} & = & \color{red}{-70x} +63 \\\Leftrightarrow & 168x \color{red}{-60} \color{blue}{+60} \color{blue}{+70x} & = & \color{red}{-70x} +63 \color{blue}{+70x} \color{blue}{+60} \\\Leftrightarrow & 168x+70x& = & 63+60 \\\Leftrightarrow & \color{red}{238} x& = & 123 \\\Leftrightarrow & x = \frac{123}{238} & & \\ & V = \left\{ \frac{123}{238} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{2})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 20x-\frac{25}{2}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{280}{ \color{blue}{14} }x- \frac{175}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{20}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 280x \color{red}{-175} & = & \color{red}{-98x} +20 \\\Leftrightarrow & 280x \color{red}{-175} \color{blue}{+175} \color{blue}{+98x} & = & \color{red}{-98x} +20 \color{blue}{+98x} \color{blue}{+175} \\\Leftrightarrow & 280x+98x& = & 20+175 \\\Leftrightarrow & \color{red}{378} x& = & 195 \\\Leftrightarrow & x = \frac{195}{378} & & \\\Leftrightarrow & x = \frac{65}{126} & & \\ & V = \left\{ \frac{65}{126} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{5}{12})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 15x+\frac{25}{12}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 12 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{180}{ \color{blue}{12} }x+ \frac{25}{ \color{blue}{12} })& = & (\frac{-24}{ \color{blue}{12} }x+ \frac{40}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 180x \color{red}{+25} & = & \color{red}{-24x} +40 \\\Leftrightarrow & 180x \color{red}{+25} \color{blue}{-25} \color{blue}{+24x} & = & \color{red}{-24x} +40 \color{blue}{+24x} \color{blue}{-25} \\\Leftrightarrow & 180x+24x& = & 40-25 \\\Leftrightarrow & \color{red}{204} x& = & 15 \\\Leftrightarrow & x = \frac{15}{204} & & \\\Leftrightarrow & x = \frac{5}{68} & & \\ & V = \left\{ \frac{5}{68} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{5}{4})& = & -4x+\frac{3}{7} \\\Leftrightarrow & 9x-\frac{15}{4}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{252}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{12}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 252x \color{red}{-105} & = & \color{red}{-112x} +12 \\\Leftrightarrow & 252x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +12 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & 252x+112x& = & 12+105 \\\Leftrightarrow & \color{red}{364} x& = & 117 \\\Leftrightarrow & x = \frac{117}{364} & & \\\Leftrightarrow & x = \frac{9}{28} & & \\ & V = \left\{ \frac{9}{28} \right\} & \\\end{align}\)