Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{7})& = & 3x+\frac{7}{8} \\\Leftrightarrow & 20x+\frac{10}{7}& = & 3x+\frac{7}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1120}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} })& = & (\frac{168}{ \color{blue}{56} }x+ \frac{49}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1120x \color{red}{+80} & = & \color{red}{168x} +49 \\\Leftrightarrow & 1120x \color{red}{+80} \color{blue}{-80} \color{blue}{-168x} & = & \color{red}{168x} +49 \color{blue}{-168x} \color{blue}{-80} \\\Leftrightarrow & 1120x-168x& = & 49-80 \\\Leftrightarrow & \color{red}{952} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{952} & & \\ & V = \left\{ \frac{-31}{952} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{2})& = & -4x+\frac{2}{3} \\\Leftrightarrow & 9x+\frac{15}{2}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 2 en 3 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{54}{ \color{blue}{6} }x+ \frac{45}{ \color{blue}{6} })& = & (\frac{-24}{ \color{blue}{6} }x+ \frac{4}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 54x \color{red}{+45} & = & \color{red}{-24x} +4 \\\Leftrightarrow & 54x \color{red}{+45} \color{blue}{-45} \color{blue}{+24x} & = & \color{red}{-24x} +4 \color{blue}{+24x} \color{blue}{-45} \\\Leftrightarrow & 54x+24x& = & 4-45 \\\Leftrightarrow & \color{red}{78} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{78} & & \\ & V = \left\{ \frac{-41}{78} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{5}{4})& = & 5x+\frac{7}{8} \\\Leftrightarrow & -12x-\frac{15}{4}& = & 5x+\frac{7}{8} \\ & & & \text{kgv van noemers 4 en 8 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-96}{ \color{blue}{8} }x- \frac{30}{ \color{blue}{8} })& = & (\frac{40}{ \color{blue}{8} }x+ \frac{7}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -96x \color{red}{-30} & = & \color{red}{40x} +7 \\\Leftrightarrow & -96x \color{red}{-30} \color{blue}{+30} \color{blue}{-40x} & = & \color{red}{40x} +7 \color{blue}{-40x} \color{blue}{+30} \\\Leftrightarrow & -96x-40x& = & 7+30 \\\Leftrightarrow & \color{red}{-136} x& = & 37 \\\Leftrightarrow & x = \frac{37}{-136} & & \\\Leftrightarrow & x = \frac{-37}{136} & & \\ & V = \left\{ \frac{-37}{136} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{5}{4})& = & 7x+\frac{10}{7} \\\Leftrightarrow & 15x-\frac{15}{4}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-105} & = & \color{red}{196x} +40 \\\Leftrightarrow & 420x \color{red}{-105} \color{blue}{+105} \color{blue}{-196x} & = & \color{red}{196x} +40 \color{blue}{-196x} \color{blue}{+105} \\\Leftrightarrow & 420x-196x& = & 40+105 \\\Leftrightarrow & \color{red}{224} x& = & 145 \\\Leftrightarrow & x = \frac{145}{224} & & \\ & V = \left\{ \frac{145}{224} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x+\frac{3}{10})& = & 5x+\frac{9}{10} \\\Leftrightarrow & -9x-\frac{9}{10}& = & 5x+\frac{9}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x- \frac{9}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{-9} & = & \color{red}{50x} +9 \\\Leftrightarrow & -90x \color{red}{-9} \color{blue}{+9} \color{blue}{-50x} & = & \color{red}{50x} +9 \color{blue}{-50x} \color{blue}{+9} \\\Leftrightarrow & -90x-50x& = & 9+9 \\\Leftrightarrow & \color{red}{-140} x& = & 18 \\\Leftrightarrow & x = \frac{18}{-140} & & \\\Leftrightarrow & x = \frac{-9}{70} & & \\ & V = \left\{ \frac{-9}{70} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{2}{7})& = & -7x+\frac{5}{6} \\\Leftrightarrow & 20x+\frac{10}{7}& = & -7x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{840}{ \color{blue}{42} }x+ \frac{60}{ \color{blue}{42} })& = & (\frac{-294}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & 840x \color{red}{+60} & = & \color{red}{-294x} +35 \\\Leftrightarrow & 840x \color{red}{+60} \color{blue}{-60} \color{blue}{+294x} & = & \color{red}{-294x} +35 \color{blue}{+294x} \color{blue}{-60} \\\Leftrightarrow & 840x+294x& = & 35-60 \\\Leftrightarrow & \color{red}{1134} x& = & -25 \\\Leftrightarrow & x = \frac{-25}{1134} & & \\ & V = \left\{ \frac{-25}{1134} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{4}{11})& = & 7x+\frac{5}{11} \\\Leftrightarrow & 30x-\frac{24}{11}& = & 7x+\frac{5}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x- \frac{24}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{5}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{-24} & = & \color{red}{77x} +5 \\\Leftrightarrow & 330x \color{red}{-24} \color{blue}{+24} \color{blue}{-77x} & = & \color{red}{77x} +5 \color{blue}{-77x} \color{blue}{+24} \\\Leftrightarrow & 330x-77x& = & 5+24 \\\Leftrightarrow & \color{red}{253} x& = & 29 \\\Leftrightarrow & x = \frac{29}{253} & & \\ & V = \left\{ \frac{29}{253} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{2}{3})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 28x-\frac{14}{3}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{588}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{12}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 588x \color{red}{-98} & = & \color{red}{105x} +12 \\\Leftrightarrow & 588x \color{red}{-98} \color{blue}{+98} \color{blue}{-105x} & = & \color{red}{105x} +12 \color{blue}{-105x} \color{blue}{+98} \\\Leftrightarrow & 588x-105x& = & 12+98 \\\Leftrightarrow & \color{red}{483} x& = & 110 \\\Leftrightarrow & x = \frac{110}{483} & & \\ & V = \left\{ \frac{110}{483} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-3x-\frac{2}{5})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 18x+\frac{12}{5}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{-245}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{+84} & = & \color{red}{-245x} +45 \\\Leftrightarrow & 630x \color{red}{+84} \color{blue}{-84} \color{blue}{+245x} & = & \color{red}{-245x} +45 \color{blue}{+245x} \color{blue}{-84} \\\Leftrightarrow & 630x+245x& = & 45-84 \\\Leftrightarrow & \color{red}{875} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{875} & & \\ & V = \left\{ \frac{-39}{875} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x-\frac{3}{7})& = & -7x+\frac{2}{11} \\\Leftrightarrow & -6x-\frac{9}{7}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x- \frac{99}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{-99} & = & \color{red}{-539x} +14 \\\Leftrightarrow & -462x \color{red}{-99} \color{blue}{+99} \color{blue}{+539x} & = & \color{red}{-539x} +14 \color{blue}{+539x} \color{blue}{+99} \\\Leftrightarrow & -462x+539x& = & 14+99 \\\Leftrightarrow & \color{red}{77} x& = & 113 \\\Leftrightarrow & x = \frac{113}{77} & & \\ & V = \left\{ \frac{113}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (5x-\frac{4}{9})& = & 7x+\frac{4}{9} \\\Leftrightarrow & -10x+\frac{8}{9}& = & 7x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-90}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -90x \color{red}{+8} & = & \color{red}{63x} +4 \\\Leftrightarrow & -90x \color{red}{+8} \color{blue}{-8} \color{blue}{-63x} & = & \color{red}{63x} +4 \color{blue}{-63x} \color{blue}{-8} \\\Leftrightarrow & -90x-63x& = & 4-8 \\\Leftrightarrow & \color{red}{-153} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-153} & & \\\Leftrightarrow & x = \frac{4}{153} & & \\ & V = \left\{ \frac{4}{153} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x+\frac{4}{11})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -20x+\frac{16}{11}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{112}{ \color{blue}{77} })& = & (\frac{693}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+112} & = & \color{red}{693x} +22 \\\Leftrightarrow & -1540x \color{red}{+112} \color{blue}{-112} \color{blue}{-693x} & = & \color{red}{693x} +22 \color{blue}{-693x} \color{blue}{-112} \\\Leftrightarrow & -1540x-693x& = & 22-112 \\\Leftrightarrow & \color{red}{-2233} x& = & -90 \\\Leftrightarrow & x = \frac{-90}{-2233} & & \\\Leftrightarrow & x = \frac{90}{2233} & & \\ & V = \left\{ \frac{90}{2233} \right\} & \\\end{align}\)