Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{3}{8})& = & 3x+\frac{5}{11} \\\Leftrightarrow & -25x+\frac{15}{8}& = & 3x+\frac{5}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-2200}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{264}{ \color{blue}{88} }x+ \frac{40}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -2200x \color{red}{+165} & = & \color{red}{264x} +40 \\\Leftrightarrow & -2200x \color{red}{+165} \color{blue}{-165} \color{blue}{-264x} & = & \color{red}{264x} +40 \color{blue}{-264x} \color{blue}{-165} \\\Leftrightarrow & -2200x-264x& = & 40-165 \\\Leftrightarrow & \color{red}{-2464} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{-2464} & & \\\Leftrightarrow & x = \frac{125}{2464} & & \\ & V = \left\{ \frac{125}{2464} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x-\frac{2}{3})& = & 7x+\frac{7}{9} \\\Leftrightarrow & -20x-\frac{10}{3}& = & 7x+\frac{7}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x- \frac{30}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{7}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{-30} & = & \color{red}{63x} +7 \\\Leftrightarrow & -180x \color{red}{-30} \color{blue}{+30} \color{blue}{-63x} & = & \color{red}{63x} +7 \color{blue}{-63x} \color{blue}{+30} \\\Leftrightarrow & -180x-63x& = & 7+30 \\\Leftrightarrow & \color{red}{-243} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-243} & & \\\Leftrightarrow & x = \frac{-37}{243} & & \\ & V = \left\{ \frac{-37}{243} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x-\frac{2}{5})& = & 8x+\frac{4}{3} \\\Leftrightarrow & -21x-\frac{14}{5}& = & 8x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-315}{ \color{blue}{15} }x- \frac{42}{ \color{blue}{15} })& = & (\frac{120}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -315x \color{red}{-42} & = & \color{red}{120x} +20 \\\Leftrightarrow & -315x \color{red}{-42} \color{blue}{+42} \color{blue}{-120x} & = & \color{red}{120x} +20 \color{blue}{-120x} \color{blue}{+42} \\\Leftrightarrow & -315x-120x& = & 20+42 \\\Leftrightarrow & \color{red}{-435} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-435} & & \\\Leftrightarrow & x = \frac{-62}{435} & & \\ & V = \left\{ \frac{-62}{435} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{5}{3})& = & -6x+\frac{5}{4} \\\Leftrightarrow & 35x+\frac{35}{3}& = & -6x+\frac{5}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x+ \frac{140}{ \color{blue}{12} })& = & (\frac{-72}{ \color{blue}{12} }x+ \frac{15}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{-72x} +15 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{+72x} & = & \color{red}{-72x} +15 \color{blue}{+72x} \color{blue}{-140} \\\Leftrightarrow & 420x+72x& = & 15-140 \\\Leftrightarrow & \color{red}{492} x& = & -125 \\\Leftrightarrow & x = \frac{-125}{492} & & \\ & V = \left\{ \frac{-125}{492} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x-\frac{5}{2})& = & 4x+\frac{6}{5} \\\Leftrightarrow & 15x-\frac{25}{2}& = & 4x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x- \frac{125}{ \color{blue}{10} })& = & (\frac{40}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{-125} & = & \color{red}{40x} +12 \\\Leftrightarrow & 150x \color{red}{-125} \color{blue}{+125} \color{blue}{-40x} & = & \color{red}{40x} +12 \color{blue}{-40x} \color{blue}{+125} \\\Leftrightarrow & 150x-40x& = & 12+125 \\\Leftrightarrow & \color{red}{110} x& = & 137 \\\Leftrightarrow & x = \frac{137}{110} & & \\ & V = \left\{ \frac{137}{110} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x+\frac{3}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 30x+\frac{18}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{2310}{ \color{blue}{77} }x+ \frac{126}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 2310x \color{red}{+126} & = & \color{red}{-539x} +88 \\\Leftrightarrow & 2310x \color{red}{+126} \color{blue}{-126} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{-126} \\\Leftrightarrow & 2310x+539x& = & 88-126 \\\Leftrightarrow & \color{red}{2849} x& = & -38 \\\Leftrightarrow & x = \frac{-38}{2849} & & \\ & V = \left\{ \frac{-38}{2849} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{3}{11})& = & -5x+\frac{3}{2} \\\Leftrightarrow & 18x+\frac{18}{11}& = & -5x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{396}{ \color{blue}{22} }x+ \frac{36}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 396x \color{red}{+36} & = & \color{red}{-110x} +33 \\\Leftrightarrow & 396x \color{red}{+36} \color{blue}{-36} \color{blue}{+110x} & = & \color{red}{-110x} +33 \color{blue}{+110x} \color{blue}{-36} \\\Leftrightarrow & 396x+110x& = & 33-36 \\\Leftrightarrow & \color{red}{506} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{506} & & \\ & V = \left\{ \frac{-3}{506} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{4}{11})& = & 3x+\frac{5}{7} \\\Leftrightarrow & -14x+\frac{28}{11}& = & 3x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1078}{ \color{blue}{77} }x+ \frac{196}{ \color{blue}{77} })& = & (\frac{231}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1078x \color{red}{+196} & = & \color{red}{231x} +55 \\\Leftrightarrow & -1078x \color{red}{+196} \color{blue}{-196} \color{blue}{-231x} & = & \color{red}{231x} +55 \color{blue}{-231x} \color{blue}{-196} \\\Leftrightarrow & -1078x-231x& = & 55-196 \\\Leftrightarrow & \color{red}{-1309} x& = & -141 \\\Leftrightarrow & x = \frac{-141}{-1309} & & \\\Leftrightarrow & x = \frac{141}{1309} & & \\ & V = \left\{ \frac{141}{1309} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (3x+\frac{2}{7})& = & 8x+\frac{8}{7} \\\Leftrightarrow & 15x+\frac{10}{7}& = & 8x+\frac{8}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{105}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} })& = & (\frac{56}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 105x \color{red}{+10} & = & \color{red}{56x} +8 \\\Leftrightarrow & 105x \color{red}{+10} \color{blue}{-10} \color{blue}{-56x} & = & \color{red}{56x} +8 \color{blue}{-56x} \color{blue}{-10} \\\Leftrightarrow & 105x-56x& = & 8-10 \\\Leftrightarrow & \color{red}{49} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{49} & & \\ & V = \left\{ \frac{-2}{49} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{3}{10})& = & 2x+\frac{7}{5} \\\Leftrightarrow & 21x+\frac{21}{10}& = & 2x+\frac{7}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{210}{ \color{blue}{10} }x+ \frac{21}{ \color{blue}{10} })& = & (\frac{20}{ \color{blue}{10} }x+ \frac{14}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 210x \color{red}{+21} & = & \color{red}{20x} +14 \\\Leftrightarrow & 210x \color{red}{+21} \color{blue}{-21} \color{blue}{-20x} & = & \color{red}{20x} +14 \color{blue}{-20x} \color{blue}{-21} \\\Leftrightarrow & 210x-20x& = & 14-21 \\\Leftrightarrow & \color{red}{190} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{190} & & \\ & V = \left\{ \frac{-7}{190} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{4}{11})& = & -2x+\frac{9}{2} \\\Leftrightarrow & 25x+\frac{20}{11}& = & -2x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x+ \frac{40}{ \color{blue}{22} })& = & (\frac{-44}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{+40} & = & \color{red}{-44x} +99 \\\Leftrightarrow & 550x \color{red}{+40} \color{blue}{-40} \color{blue}{+44x} & = & \color{red}{-44x} +99 \color{blue}{+44x} \color{blue}{-40} \\\Leftrightarrow & 550x+44x& = & 99-40 \\\Leftrightarrow & \color{red}{594} x& = & 59 \\\Leftrightarrow & x = \frac{59}{594} & & \\ & V = \left\{ \frac{59}{594} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{5}{3})& = & -9x+\frac{9}{2} \\\Leftrightarrow & 10x+\frac{10}{3}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 3 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x+ \frac{20}{ \color{blue}{6} })& = & (\frac{-54}{ \color{blue}{6} }x+ \frac{27}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{+20} & = & \color{red}{-54x} +27 \\\Leftrightarrow & 60x \color{red}{+20} \color{blue}{-20} \color{blue}{+54x} & = & \color{red}{-54x} +27 \color{blue}{+54x} \color{blue}{-20} \\\Leftrightarrow & 60x+54x& = & 27-20 \\\Leftrightarrow & \color{red}{114} x& = & 7 \\\Leftrightarrow & x = \frac{7}{114} & & \\ & V = \left\{ \frac{7}{114} \right\} & \\\end{align}\)