Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{4})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -6x+\frac{9}{4}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 4 en 2 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-24}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{10}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -24x \color{red}{+9} & = & \color{red}{28x} +10 \\\Leftrightarrow & -24x \color{red}{+9} \color{blue}{-9} \color{blue}{-28x} & = & \color{red}{28x} +10 \color{blue}{-28x} \color{blue}{-9} \\\Leftrightarrow & -24x-28x& = & 10-9 \\\Leftrightarrow & \color{red}{-52} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-52} & & \\\Leftrightarrow & x = \frac{-1}{52} & & \\ & V = \left\{ \frac{-1}{52} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{11})& = & 4x+\frac{8}{7} \\\Leftrightarrow & -15x+\frac{15}{11}& = & 4x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1155}{ \color{blue}{77} }x+ \frac{105}{ \color{blue}{77} })& = & (\frac{308}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1155x \color{red}{+105} & = & \color{red}{308x} +88 \\\Leftrightarrow & -1155x \color{red}{+105} \color{blue}{-105} \color{blue}{-308x} & = & \color{red}{308x} +88 \color{blue}{-308x} \color{blue}{-105} \\\Leftrightarrow & -1155x-308x& = & 88-105 \\\Leftrightarrow & \color{red}{-1463} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-1463} & & \\\Leftrightarrow & x = \frac{17}{1463} & & \\ & V = \left\{ \frac{17}{1463} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{5}{9})& = & 3x+\frac{2}{5} \\\Leftrightarrow & -14x-\frac{35}{9}& = & 3x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-630}{ \color{blue}{45} }x- \frac{175}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -630x \color{red}{-175} & = & \color{red}{135x} +18 \\\Leftrightarrow & -630x \color{red}{-175} \color{blue}{+175} \color{blue}{-135x} & = & \color{red}{135x} +18 \color{blue}{-135x} \color{blue}{+175} \\\Leftrightarrow & -630x-135x& = & 18+175 \\\Leftrightarrow & \color{red}{-765} x& = & 193 \\\Leftrightarrow & x = \frac{193}{-765} & & \\\Leftrightarrow & x = \frac{-193}{765} & & \\ & V = \left\{ \frac{-193}{765} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & -2x+\frac{4}{3} \\\Leftrightarrow & 9x-\frac{6}{11}& = & -2x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{-18} & = & \color{red}{-66x} +44 \\\Leftrightarrow & 297x \color{red}{-18} \color{blue}{+18} \color{blue}{+66x} & = & \color{red}{-66x} +44 \color{blue}{+66x} \color{blue}{+18} \\\Leftrightarrow & 297x+66x& = & 44+18 \\\Leftrightarrow & \color{red}{363} x& = & 62 \\\Leftrightarrow & x = \frac{62}{363} & & \\ & V = \left\{ \frac{62}{363} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{2}{5})& = & -7x+\frac{6}{7} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -7x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-84} & = & \color{red}{-245x} +30 \\\Leftrightarrow & 420x \color{red}{-84} \color{blue}{+84} \color{blue}{+245x} & = & \color{red}{-245x} +30 \color{blue}{+245x} \color{blue}{+84} \\\Leftrightarrow & 420x+245x& = & 30+84 \\\Leftrightarrow & \color{red}{665} x& = & 114 \\\Leftrightarrow & x = \frac{114}{665} & & \\\Leftrightarrow & x = \frac{6}{35} & & \\ & V = \left\{ \frac{6}{35} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (5x+\frac{2}{3})& = & -3x+\frac{7}{4} \\\Leftrightarrow & -20x-\frac{8}{3}& = & -3x+\frac{7}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-240}{ \color{blue}{12} }x- \frac{32}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{21}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -240x \color{red}{-32} & = & \color{red}{-36x} +21 \\\Leftrightarrow & -240x \color{red}{-32} \color{blue}{+32} \color{blue}{+36x} & = & \color{red}{-36x} +21 \color{blue}{+36x} \color{blue}{+32} \\\Leftrightarrow & -240x+36x& = & 21+32 \\\Leftrightarrow & \color{red}{-204} x& = & 53 \\\Leftrightarrow & x = \frac{53}{-204} & & \\\Leftrightarrow & x = \frac{-53}{204} & & \\ & V = \left\{ \frac{-53}{204} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{5})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -30x-\frac{18}{5}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-1050}{ \color{blue}{35} }x- \frac{126}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{15}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -1050x \color{red}{-126} & = & \color{red}{245x} +15 \\\Leftrightarrow & -1050x \color{red}{-126} \color{blue}{+126} \color{blue}{-245x} & = & \color{red}{245x} +15 \color{blue}{-245x} \color{blue}{+126} \\\Leftrightarrow & -1050x-245x& = & 15+126 \\\Leftrightarrow & \color{red}{-1295} x& = & 141 \\\Leftrightarrow & x = \frac{141}{-1295} & & \\\Leftrightarrow & x = \frac{-141}{1295} & & \\ & V = \left\{ \frac{-141}{1295} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x-\frac{2}{9})& = & 5x+\frac{8}{3} \\\Leftrightarrow & 8x-\frac{4}{9}& = & 5x+\frac{8}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{24}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{-4} & = & \color{red}{45x} +24 \\\Leftrightarrow & 72x \color{red}{-4} \color{blue}{+4} \color{blue}{-45x} & = & \color{red}{45x} +24 \color{blue}{-45x} \color{blue}{+4} \\\Leftrightarrow & 72x-45x& = & 24+4 \\\Leftrightarrow & \color{red}{27} x& = & 28 \\\Leftrightarrow & x = \frac{28}{27} & & \\ & V = \left\{ \frac{28}{27} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{5}{9})& = & -7x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{20}{9}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{900}{ \color{blue}{45} }x- \frac{100}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{54}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 900x \color{red}{-100} & = & \color{red}{-315x} +54 \\\Leftrightarrow & 900x \color{red}{-100} \color{blue}{+100} \color{blue}{+315x} & = & \color{red}{-315x} +54 \color{blue}{+315x} \color{blue}{+100} \\\Leftrightarrow & 900x+315x& = & 54+100 \\\Leftrightarrow & \color{red}{1215} x& = & 154 \\\Leftrightarrow & x = \frac{154}{1215} & & \\ & V = \left\{ \frac{154}{1215} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{4}{11})& = & -9x+\frac{9}{4} \\\Leftrightarrow & -8x-\frac{16}{11}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-352}{ \color{blue}{44} }x- \frac{64}{ \color{blue}{44} })& = & (\frac{-396}{ \color{blue}{44} }x+ \frac{99}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -352x \color{red}{-64} & = & \color{red}{-396x} +99 \\\Leftrightarrow & -352x \color{red}{-64} \color{blue}{+64} \color{blue}{+396x} & = & \color{red}{-396x} +99 \color{blue}{+396x} \color{blue}{+64} \\\Leftrightarrow & -352x+396x& = & 99+64 \\\Leftrightarrow & \color{red}{44} x& = & 163 \\\Leftrightarrow & x = \frac{163}{44} & & \\ & V = \left\{ \frac{163}{44} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{5}{6})& = & 2x+\frac{8}{9} \\\Leftrightarrow & 15x+\frac{25}{6}& = & 2x+\frac{8}{9} \\ & & & \text{kgv van noemers 6 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{270}{ \color{blue}{18} }x+ \frac{75}{ \color{blue}{18} })& = & (\frac{36}{ \color{blue}{18} }x+ \frac{16}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & 270x \color{red}{+75} & = & \color{red}{36x} +16 \\\Leftrightarrow & 270x \color{red}{+75} \color{blue}{-75} \color{blue}{-36x} & = & \color{red}{36x} +16 \color{blue}{-36x} \color{blue}{-75} \\\Leftrightarrow & 270x-36x& = & 16-75 \\\Leftrightarrow & \color{red}{234} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{234} & & \\ & V = \left\{ \frac{-59}{234} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{3})& = & 2x+\frac{4}{5} \\\Leftrightarrow & 35x+\frac{28}{3}& = & 2x+\frac{4}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{525}{ \color{blue}{15} }x+ \frac{140}{ \color{blue}{15} })& = & (\frac{30}{ \color{blue}{15} }x+ \frac{12}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 525x \color{red}{+140} & = & \color{red}{30x} +12 \\\Leftrightarrow & 525x \color{red}{+140} \color{blue}{-140} \color{blue}{-30x} & = & \color{red}{30x} +12 \color{blue}{-30x} \color{blue}{-140} \\\Leftrightarrow & 525x-30x& = & 12-140 \\\Leftrightarrow & \color{red}{495} x& = & -128 \\\Leftrightarrow & x = \frac{-128}{495} & & \\ & V = \left\{ \frac{-128}{495} \right\} & \\\end{align}\)