Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{5}{2})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 25x-\frac{25}{2}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{550}{ \color{blue}{22} }x- \frac{275}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 550x \color{red}{-275} & = & \color{red}{-154x} +4 \\\Leftrightarrow & 550x \color{red}{-275} \color{blue}{+275} \color{blue}{+154x} & = & \color{red}{-154x} +4 \color{blue}{+154x} \color{blue}{+275} \\\Leftrightarrow & 550x+154x& = & 4+275 \\\Leftrightarrow & \color{red}{704} x& = & 279 \\\Leftrightarrow & x = \frac{279}{704} & & \\ & V = \left\{ \frac{279}{704} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{3}{8})& = & 6x+\frac{10}{7} \\\Leftrightarrow & 35x+\frac{21}{8}& = & 6x+\frac{10}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1960}{ \color{blue}{56} }x+ \frac{147}{ \color{blue}{56} })& = & (\frac{336}{ \color{blue}{56} }x+ \frac{80}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1960x \color{red}{+147} & = & \color{red}{336x} +80 \\\Leftrightarrow & 1960x \color{red}{+147} \color{blue}{-147} \color{blue}{-336x} & = & \color{red}{336x} +80 \color{blue}{-336x} \color{blue}{-147} \\\Leftrightarrow & 1960x-336x& = & 80-147 \\\Leftrightarrow & \color{red}{1624} x& = & -67 \\\Leftrightarrow & x = \frac{-67}{1624} & & \\ & V = \left\{ \frac{-67}{1624} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x+\frac{4}{11})& = & -7x+\frac{8}{7} \\\Leftrightarrow & 10x+\frac{20}{11}& = & -7x+\frac{8}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{88}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{+140} & = & \color{red}{-539x} +88 \\\Leftrightarrow & 770x \color{red}{+140} \color{blue}{-140} \color{blue}{+539x} & = & \color{red}{-539x} +88 \color{blue}{+539x} \color{blue}{-140} \\\Leftrightarrow & 770x+539x& = & 88-140 \\\Leftrightarrow & \color{red}{1309} x& = & -52 \\\Leftrightarrow & x = \frac{-52}{1309} & & \\ & V = \left\{ \frac{-52}{1309} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{7})& = & 7x+\frac{10}{7} \\\Leftrightarrow & -10x+\frac{4}{7}& = & 7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-70}{ \color{blue}{7} }x+ \frac{4}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -70x \color{red}{+4} & = & \color{red}{49x} +10 \\\Leftrightarrow & -70x \color{red}{+4} \color{blue}{-4} \color{blue}{-49x} & = & \color{red}{49x} +10 \color{blue}{-49x} \color{blue}{-4} \\\Leftrightarrow & -70x-49x& = & 10-4 \\\Leftrightarrow & \color{red}{-119} x& = & 6 \\\Leftrightarrow & x = \frac{6}{-119} & & \\\Leftrightarrow & x = \frac{-6}{119} & & \\ & V = \left\{ \frac{-6}{119} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x+\frac{4}{3})& = & -5x+\frac{9}{4} \\\Leftrightarrow & 6x+\frac{8}{3}& = & -5x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{72}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} })& = & (\frac{-60}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 72x \color{red}{+32} & = & \color{red}{-60x} +27 \\\Leftrightarrow & 72x \color{red}{+32} \color{blue}{-32} \color{blue}{+60x} & = & \color{red}{-60x} +27 \color{blue}{+60x} \color{blue}{-32} \\\Leftrightarrow & 72x+60x& = & 27-32 \\\Leftrightarrow & \color{red}{132} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{132} & & \\ & V = \left\{ \frac{-5}{132} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{132}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-132} & = & \color{red}{-385x} +10 \\\Leftrightarrow & 440x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +10 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & 440x+385x& = & 10+132 \\\Leftrightarrow & \color{red}{825} x& = & 142 \\\Leftrightarrow & x = \frac{142}{825} & & \\ & V = \left\{ \frac{142}{825} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 8x-\frac{16}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{80}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-80} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 280x \color{red}{-80} \color{blue}{+80} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+80} \\\Leftrightarrow & 280x+175x& = & 42+80 \\\Leftrightarrow & \color{red}{455} x& = & 122 \\\Leftrightarrow & x = \frac{122}{455} & & \\ & V = \left\{ \frac{122}{455} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{7})& = & -5x+\frac{5}{11} \\\Leftrightarrow & -12x-\frac{12}{7}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x- \frac{132}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{35}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{-132} & = & \color{red}{-385x} +35 \\\Leftrightarrow & -924x \color{red}{-132} \color{blue}{+132} \color{blue}{+385x} & = & \color{red}{-385x} +35 \color{blue}{+385x} \color{blue}{+132} \\\Leftrightarrow & -924x+385x& = & 35+132 \\\Leftrightarrow & \color{red}{-539} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-539} & & \\\Leftrightarrow & x = \frac{-167}{539} & & \\ & V = \left\{ \frac{-167}{539} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x-\frac{4}{7})& = & 9x+\frac{5}{6} \\\Leftrightarrow & -8x-\frac{16}{7}& = & 9x+\frac{5}{6} \\ & & & \text{kgv van noemers 7 en 6 is 42} \\\Leftrightarrow & \color{blue}{42} .(\frac{-336}{ \color{blue}{42} }x- \frac{96}{ \color{blue}{42} })& = & (\frac{378}{ \color{blue}{42} }x+ \frac{35}{ \color{blue}{42} }). \color{blue}{42} \\\Leftrightarrow & -336x \color{red}{-96} & = & \color{red}{378x} +35 \\\Leftrightarrow & -336x \color{red}{-96} \color{blue}{+96} \color{blue}{-378x} & = & \color{red}{378x} +35 \color{blue}{-378x} \color{blue}{+96} \\\Leftrightarrow & -336x-378x& = & 35+96 \\\Leftrightarrow & \color{red}{-714} x& = & 131 \\\Leftrightarrow & x = \frac{131}{-714} & & \\\Leftrightarrow & x = \frac{-131}{714} & & \\ & V = \left\{ \frac{-131}{714} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{5}{8})& = & -8x+\frac{4}{7} \\\Leftrightarrow & 35x+\frac{35}{8}& = & -8x+\frac{4}{7} \\ & & & \text{kgv van noemers 8 en 7 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{1960}{ \color{blue}{56} }x+ \frac{245}{ \color{blue}{56} })& = & (\frac{-448}{ \color{blue}{56} }x+ \frac{32}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & 1960x \color{red}{+245} & = & \color{red}{-448x} +32 \\\Leftrightarrow & 1960x \color{red}{+245} \color{blue}{-245} \color{blue}{+448x} & = & \color{red}{-448x} +32 \color{blue}{+448x} \color{blue}{-245} \\\Leftrightarrow & 1960x+448x& = & 32-245 \\\Leftrightarrow & \color{red}{2408} x& = & -213 \\\Leftrightarrow & x = \frac{-213}{2408} & & \\ & V = \left\{ \frac{-213}{2408} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x-\frac{3}{7})& = & 7x+\frac{2}{7} \\\Leftrightarrow & -30x-\frac{18}{7}& = & 7x+\frac{2}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x- \frac{18}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{2}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{-18} & = & \color{red}{49x} +2 \\\Leftrightarrow & -210x \color{red}{-18} \color{blue}{+18} \color{blue}{-49x} & = & \color{red}{49x} +2 \color{blue}{-49x} \color{blue}{+18} \\\Leftrightarrow & -210x-49x& = & 2+18 \\\Leftrightarrow & \color{red}{-259} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-259} & & \\\Leftrightarrow & x = \frac{-20}{259} & & \\ & V = \left\{ \frac{-20}{259} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{10})& = & 7x+\frac{4}{5} \\\Leftrightarrow & 15x+\frac{9}{10}& = & 7x+\frac{4}{5} \\ & & & \text{kgv van noemers 10 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{150}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{8}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 150x \color{red}{+9} & = & \color{red}{70x} +8 \\\Leftrightarrow & 150x \color{red}{+9} \color{blue}{-9} \color{blue}{-70x} & = & \color{red}{70x} +8 \color{blue}{-70x} \color{blue}{-9} \\\Leftrightarrow & 150x-70x& = & 8-9 \\\Leftrightarrow & \color{red}{80} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{80} & & \\ & V = \left\{ \frac{-1}{80} \right\} & \\\end{align}\)