Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-3x+\frac{3}{8})& = & 8x+\frac{3}{2} \\\Leftrightarrow & 21x-\frac{21}{8}& = & 8x+\frac{3}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{168}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{64}{ \color{blue}{8} }x+ \frac{12}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 168x \color{red}{-21} & = & \color{red}{64x} +12 \\\Leftrightarrow & 168x \color{red}{-21} \color{blue}{+21} \color{blue}{-64x} & = & \color{red}{64x} +12 \color{blue}{-64x} \color{blue}{+21} \\\Leftrightarrow & 168x-64x& = & 12+21 \\\Leftrightarrow & \color{red}{104} x& = & 33 \\\Leftrightarrow & x = \frac{33}{104} & & \\ & V = \left\{ \frac{33}{104} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{3}{7})& = & 9x+\frac{8}{5} \\\Leftrightarrow & -4x+\frac{6}{7}& = & 9x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-140}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -140x \color{red}{+30} & = & \color{red}{315x} +56 \\\Leftrightarrow & -140x \color{red}{+30} \color{blue}{-30} \color{blue}{-315x} & = & \color{red}{315x} +56 \color{blue}{-315x} \color{blue}{-30} \\\Leftrightarrow & -140x-315x& = & 56-30 \\\Leftrightarrow & \color{red}{-455} x& = & 26 \\\Leftrightarrow & x = \frac{26}{-455} & & \\\Leftrightarrow & x = \frac{-2}{35} & & \\ & V = \left\{ \frac{-2}{35} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{4}{5})& = & 5x+\frac{4}{7} \\\Leftrightarrow & 6x+\frac{12}{5}& = & 5x+\frac{4}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{210}{ \color{blue}{35} }x+ \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{20}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 210x \color{red}{+84} & = & \color{red}{175x} +20 \\\Leftrightarrow & 210x \color{red}{+84} \color{blue}{-84} \color{blue}{-175x} & = & \color{red}{175x} +20 \color{blue}{-175x} \color{blue}{-84} \\\Leftrightarrow & 210x-175x& = & 20-84 \\\Leftrightarrow & \color{red}{35} x& = & -64 \\\Leftrightarrow & x = \frac{-64}{35} & & \\ & V = \left\{ \frac{-64}{35} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{5}{3})& = & -5x+\frac{5}{7} \\\Leftrightarrow & 6x-\frac{10}{3}& = & -5x+\frac{5}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{126}{ \color{blue}{21} }x- \frac{70}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{15}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 126x \color{red}{-70} & = & \color{red}{-105x} +15 \\\Leftrightarrow & 126x \color{red}{-70} \color{blue}{+70} \color{blue}{+105x} & = & \color{red}{-105x} +15 \color{blue}{+105x} \color{blue}{+70} \\\Leftrightarrow & 126x+105x& = & 15+70 \\\Leftrightarrow & \color{red}{231} x& = & 85 \\\Leftrightarrow & x = \frac{85}{231} & & \\ & V = \left\{ \frac{85}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x+\frac{5}{11})& = & -5x+\frac{10}{7} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -5x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{210}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-210} & = & \color{red}{-385x} +110 \\\Leftrightarrow & 924x \color{red}{-210} \color{blue}{+210} \color{blue}{+385x} & = & \color{red}{-385x} +110 \color{blue}{+385x} \color{blue}{+210} \\\Leftrightarrow & 924x+385x& = & 110+210 \\\Leftrightarrow & \color{red}{1309} x& = & 320 \\\Leftrightarrow & x = \frac{320}{1309} & & \\ & V = \left\{ \frac{320}{1309} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{11})& = & -7x+\frac{4}{3} \\\Leftrightarrow & 18x-\frac{12}{11}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{594}{ \color{blue}{33} }x- \frac{36}{ \color{blue}{33} })& = & (\frac{-231}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 594x \color{red}{-36} & = & \color{red}{-231x} +44 \\\Leftrightarrow & 594x \color{red}{-36} \color{blue}{+36} \color{blue}{+231x} & = & \color{red}{-231x} +44 \color{blue}{+231x} \color{blue}{+36} \\\Leftrightarrow & 594x+231x& = & 44+36 \\\Leftrightarrow & \color{red}{825} x& = & 80 \\\Leftrightarrow & x = \frac{80}{825} & & \\\Leftrightarrow & x = \frac{16}{165} & & \\ & V = \left\{ \frac{16}{165} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -24x+\frac{30}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-840}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -840x \color{red}{+150} & = & \color{red}{175x} +42 \\\Leftrightarrow & -840x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -840x-175x& = & 42-150 \\\Leftrightarrow & \color{red}{-1015} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-1015} & & \\\Leftrightarrow & x = \frac{108}{1015} & & \\ & V = \left\{ \frac{108}{1015} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{4}{5})& = & -7x+\frac{7}{8} \\\Leftrightarrow & -30x+\frac{24}{5}& = & -7x+\frac{7}{8} \\ & & & \text{kgv van noemers 5 en 8 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{-1200}{ \color{blue}{40} }x+ \frac{192}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{35}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & -1200x \color{red}{+192} & = & \color{red}{-280x} +35 \\\Leftrightarrow & -1200x \color{red}{+192} \color{blue}{-192} \color{blue}{+280x} & = & \color{red}{-280x} +35 \color{blue}{+280x} \color{blue}{-192} \\\Leftrightarrow & -1200x+280x& = & 35-192 \\\Leftrightarrow & \color{red}{-920} x& = & -157 \\\Leftrightarrow & x = \frac{-157}{-920} & & \\\Leftrightarrow & x = \frac{157}{920} & & \\ & V = \left\{ \frac{157}{920} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{2})& = & 9x+\frac{2}{11} \\\Leftrightarrow & 35x+\frac{7}{2}& = & 9x+\frac{2}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{770}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} })& = & (\frac{198}{ \color{blue}{22} }x+ \frac{4}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 770x \color{red}{+77} & = & \color{red}{198x} +4 \\\Leftrightarrow & 770x \color{red}{+77} \color{blue}{-77} \color{blue}{-198x} & = & \color{red}{198x} +4 \color{blue}{-198x} \color{blue}{-77} \\\Leftrightarrow & 770x-198x& = & 4-77 \\\Leftrightarrow & \color{red}{572} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{572} & & \\ & V = \left\{ \frac{-73}{572} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{4}{3})& = & 3x+\frac{6}{7} \\\Leftrightarrow & 20x-\frac{16}{3}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x- \frac{112}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{-112} & = & \color{red}{63x} +18 \\\Leftrightarrow & 420x \color{red}{-112} \color{blue}{+112} \color{blue}{-63x} & = & \color{red}{63x} +18 \color{blue}{-63x} \color{blue}{+112} \\\Leftrightarrow & 420x-63x& = & 18+112 \\\Leftrightarrow & \color{red}{357} x& = & 130 \\\Leftrightarrow & x = \frac{130}{357} & & \\ & V = \left\{ \frac{130}{357} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{3}{11})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -30x-\frac{18}{11}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-660}{ \color{blue}{22} }x- \frac{36}{ \color{blue}{22} })& = & (\frac{-154}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -660x \color{red}{-36} & = & \color{red}{-154x} +99 \\\Leftrightarrow & -660x \color{red}{-36} \color{blue}{+36} \color{blue}{+154x} & = & \color{red}{-154x} +99 \color{blue}{+154x} \color{blue}{+36} \\\Leftrightarrow & -660x+154x& = & 99+36 \\\Leftrightarrow & \color{red}{-506} x& = & 135 \\\Leftrightarrow & x = \frac{135}{-506} & & \\\Leftrightarrow & x = \frac{-135}{506} & & \\ & V = \left\{ \frac{-135}{506} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{11})& = & -9x+\frac{9}{7} \\\Leftrightarrow & -20x+\frac{20}{11}& = & -9x+\frac{9}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1540}{ \color{blue}{77} }x+ \frac{140}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1540x \color{red}{+140} & = & \color{red}{-693x} +99 \\\Leftrightarrow & -1540x \color{red}{+140} \color{blue}{-140} \color{blue}{+693x} & = & \color{red}{-693x} +99 \color{blue}{+693x} \color{blue}{-140} \\\Leftrightarrow & -1540x+693x& = & 99-140 \\\Leftrightarrow & \color{red}{-847} x& = & -41 \\\Leftrightarrow & x = \frac{-41}{-847} & & \\\Leftrightarrow & x = \frac{41}{847} & & \\ & V = \left\{ \frac{41}{847} \right\} & \\\end{align}\)