Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x+\frac{2}{11})& = & 7x+\frac{3}{8} \\\Leftrightarrow & 18x+\frac{12}{11}& = & 7x+\frac{3}{8} \\ & & & \text{kgv van noemers 11 en 8 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{1584}{ \color{blue}{88} }x+ \frac{96}{ \color{blue}{88} })& = & (\frac{616}{ \color{blue}{88} }x+ \frac{33}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & 1584x \color{red}{+96} & = & \color{red}{616x} +33 \\\Leftrightarrow & 1584x \color{red}{+96} \color{blue}{-96} \color{blue}{-616x} & = & \color{red}{616x} +33 \color{blue}{-616x} \color{blue}{-96} \\\Leftrightarrow & 1584x-616x& = & 33-96 \\\Leftrightarrow & \color{red}{968} x& = & -63 \\\Leftrightarrow & x = \frac{-63}{968} & & \\ & V = \left\{ \frac{-63}{968} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{11})& = & -4x+\frac{2}{3} \\\Leftrightarrow & -15x-\frac{6}{11}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-495}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-132}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -495x \color{red}{-18} & = & \color{red}{-132x} +22 \\\Leftrightarrow & -495x \color{red}{-18} \color{blue}{+18} \color{blue}{+132x} & = & \color{red}{-132x} +22 \color{blue}{+132x} \color{blue}{+18} \\\Leftrightarrow & -495x+132x& = & 22+18 \\\Leftrightarrow & \color{red}{-363} x& = & 40 \\\Leftrightarrow & x = \frac{40}{-363} & & \\\Leftrightarrow & x = \frac{-40}{363} & & \\ & V = \left\{ \frac{-40}{363} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{9})& = & -2x+\frac{2}{5} \\\Leftrightarrow & 35x+\frac{28}{9}& = & -2x+\frac{2}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1575}{ \color{blue}{45} }x+ \frac{140}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{18}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1575x \color{red}{+140} & = & \color{red}{-90x} +18 \\\Leftrightarrow & 1575x \color{red}{+140} \color{blue}{-140} \color{blue}{+90x} & = & \color{red}{-90x} +18 \color{blue}{+90x} \color{blue}{-140} \\\Leftrightarrow & 1575x+90x& = & 18-140 \\\Leftrightarrow & \color{red}{1665} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{1665} & & \\ & V = \left\{ \frac{-122}{1665} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{12})& = & -9x+\frac{3}{8} \\\Leftrightarrow & 28x-\frac{35}{12}& = & -9x+\frac{3}{8} \\ & & & \text{kgv van noemers 12 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{672}{ \color{blue}{24} }x- \frac{70}{ \color{blue}{24} })& = & (\frac{-216}{ \color{blue}{24} }x+ \frac{9}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 672x \color{red}{-70} & = & \color{red}{-216x} +9 \\\Leftrightarrow & 672x \color{red}{-70} \color{blue}{+70} \color{blue}{+216x} & = & \color{red}{-216x} +9 \color{blue}{+216x} \color{blue}{+70} \\\Leftrightarrow & 672x+216x& = & 9+70 \\\Leftrightarrow & \color{red}{888} x& = & 79 \\\Leftrightarrow & x = \frac{79}{888} & & \\ & V = \left\{ \frac{79}{888} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{5}{3})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 6x+\frac{10}{3}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{198}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 198x \color{red}{+110} & = & \color{red}{231x} +15 \\\Leftrightarrow & 198x \color{red}{+110} \color{blue}{-110} \color{blue}{-231x} & = & \color{red}{231x} +15 \color{blue}{-231x} \color{blue}{-110} \\\Leftrightarrow & 198x-231x& = & 15-110 \\\Leftrightarrow & \color{red}{-33} x& = & -95 \\\Leftrightarrow & x = \frac{-95}{-33} & & \\\Leftrightarrow & x = \frac{95}{33} & & \\ & V = \left\{ \frac{95}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & 7x+\frac{9}{10} \\\Leftrightarrow & -6x+\frac{6}{11}& = & 7x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-660}{ \color{blue}{110} }x+ \frac{60}{ \color{blue}{110} })& = & (\frac{770}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -660x \color{red}{+60} & = & \color{red}{770x} +99 \\\Leftrightarrow & -660x \color{red}{+60} \color{blue}{-60} \color{blue}{-770x} & = & \color{red}{770x} +99 \color{blue}{-770x} \color{blue}{-60} \\\Leftrightarrow & -660x-770x& = & 99-60 \\\Leftrightarrow & \color{red}{-1430} x& = & 39 \\\Leftrightarrow & x = \frac{39}{-1430} & & \\\Leftrightarrow & x = \frac{-3}{110} & & \\ & V = \left\{ \frac{-3}{110} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x-\frac{2}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 4x-\frac{4}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{56}{ \color{blue}{14} }x- \frac{8}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 56x \color{red}{-8} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 56x \color{red}{-8} \color{blue}{+8} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{+8} \\\Leftrightarrow & 56x+70x& = & 35+8 \\\Leftrightarrow & \color{red}{126} x& = & 43 \\\Leftrightarrow & x = \frac{43}{126} & & \\ & V = \left\{ \frac{43}{126} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x+\frac{4}{5})& = & -7x+\frac{4}{11} \\\Leftrightarrow & 30x-\frac{24}{5}& = & -7x+\frac{4}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1650}{ \color{blue}{55} }x- \frac{264}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{20}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1650x \color{red}{-264} & = & \color{red}{-385x} +20 \\\Leftrightarrow & 1650x \color{red}{-264} \color{blue}{+264} \color{blue}{+385x} & = & \color{red}{-385x} +20 \color{blue}{+385x} \color{blue}{+264} \\\Leftrightarrow & 1650x+385x& = & 20+264 \\\Leftrightarrow & \color{red}{2035} x& = & 284 \\\Leftrightarrow & x = \frac{284}{2035} & & \\ & V = \left\{ \frac{284}{2035} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+1)& = & -7x+\frac{9}{4} \\\Leftrightarrow & -10x-5& = & -7x+\frac{9}{4} \\ & & & \text{kgv van noemers 1 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-40}{ \color{blue}{4} }x- \frac{20}{ \color{blue}{4} })& = & (\frac{-28}{ \color{blue}{4} }x+ \frac{9}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -40x \color{red}{-20} & = & \color{red}{-28x} +9 \\\Leftrightarrow & -40x \color{red}{-20} \color{blue}{+20} \color{blue}{+28x} & = & \color{red}{-28x} +9 \color{blue}{+28x} \color{blue}{+20} \\\Leftrightarrow & -40x+28x& = & 9+20 \\\Leftrightarrow & \color{red}{-12} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-12} & & \\\Leftrightarrow & x = \frac{-29}{12} & & \\ & V = \left\{ \frac{-29}{12} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x+\frac{4}{3})& = & 7x+\frac{5}{8} \\\Leftrightarrow & 6x-\frac{8}{3}& = & 7x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{144}{ \color{blue}{24} }x- \frac{64}{ \color{blue}{24} })& = & (\frac{168}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 144x \color{red}{-64} & = & \color{red}{168x} +15 \\\Leftrightarrow & 144x \color{red}{-64} \color{blue}{+64} \color{blue}{-168x} & = & \color{red}{168x} +15 \color{blue}{-168x} \color{blue}{+64} \\\Leftrightarrow & 144x-168x& = & 15+64 \\\Leftrightarrow & \color{red}{-24} x& = & 79 \\\Leftrightarrow & x = \frac{79}{-24} & & \\\Leftrightarrow & x = \frac{-79}{24} & & \\ & V = \left\{ \frac{-79}{24} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x-\frac{5}{4})& = & -8x+\frac{2}{3} \\\Leftrightarrow & -21x+\frac{35}{4}& = & -8x+\frac{2}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x+ \frac{105}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{8}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{+105} & = & \color{red}{-96x} +8 \\\Leftrightarrow & -252x \color{red}{+105} \color{blue}{-105} \color{blue}{+96x} & = & \color{red}{-96x} +8 \color{blue}{+96x} \color{blue}{-105} \\\Leftrightarrow & -252x+96x& = & 8-105 \\\Leftrightarrow & \color{red}{-156} x& = & -97 \\\Leftrightarrow & x = \frac{-97}{-156} & & \\\Leftrightarrow & x = \frac{97}{156} & & \\ & V = \left\{ \frac{97}{156} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x+\frac{5}{3})& = & 7x+\frac{5}{7} \\\Leftrightarrow & 25x+\frac{25}{3}& = & 7x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{175}{ \color{blue}{21} })& = & (\frac{147}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+175} & = & \color{red}{147x} +15 \\\Leftrightarrow & 525x \color{red}{+175} \color{blue}{-175} \color{blue}{-147x} & = & \color{red}{147x} +15 \color{blue}{-147x} \color{blue}{-175} \\\Leftrightarrow & 525x-147x& = & 15-175 \\\Leftrightarrow & \color{red}{378} x& = & -160 \\\Leftrightarrow & x = \frac{-160}{378} & & \\\Leftrightarrow & x = \frac{-80}{189} & & \\ & V = \left\{ \frac{-80}{189} \right\} & \\\end{align}\)