Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x+\frac{2}{3})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{8}{3}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{36}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{-15}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 36x \color{red}{+8} & = & \color{red}{-15x} +4 \\\Leftrightarrow & 36x \color{red}{+8} \color{blue}{-8} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{-8} \\\Leftrightarrow & 36x+15x& = & 4-8 \\\Leftrightarrow & \color{red}{51} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{51} & & \\ & V = \left\{ \frac{-4}{51} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{5}{7})& = & 3x+\frac{5}{12} \\\Leftrightarrow & 10x+\frac{10}{7}& = & 3x+\frac{5}{12} \\ & & & \text{kgv van noemers 7 en 12 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{840}{ \color{blue}{84} }x+ \frac{120}{ \color{blue}{84} })& = & (\frac{252}{ \color{blue}{84} }x+ \frac{35}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 840x \color{red}{+120} & = & \color{red}{252x} +35 \\\Leftrightarrow & 840x \color{red}{+120} \color{blue}{-120} \color{blue}{-252x} & = & \color{red}{252x} +35 \color{blue}{-252x} \color{blue}{-120} \\\Leftrightarrow & 840x-252x& = & 35-120 \\\Leftrightarrow & \color{red}{588} x& = & -85 \\\Leftrightarrow & x = \frac{-85}{588} & & \\ & V = \left\{ \frac{-85}{588} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{2})& = & -5x+\frac{4}{11} \\\Leftrightarrow & 12x-\frac{9}{2}& = & -5x+\frac{4}{11} \\ & & & \text{kgv van noemers 2 en 11 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{264}{ \color{blue}{22} }x- \frac{99}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{8}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 264x \color{red}{-99} & = & \color{red}{-110x} +8 \\\Leftrightarrow & 264x \color{red}{-99} \color{blue}{+99} \color{blue}{+110x} & = & \color{red}{-110x} +8 \color{blue}{+110x} \color{blue}{+99} \\\Leftrightarrow & 264x+110x& = & 8+99 \\\Leftrightarrow & \color{red}{374} x& = & 107 \\\Leftrightarrow & x = \frac{107}{374} & & \\ & V = \left\{ \frac{107}{374} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x+\frac{3}{11})& = & -3x+\frac{2}{9} \\\Leftrightarrow & 14x+\frac{21}{11}& = & -3x+\frac{2}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{1386}{ \color{blue}{99} }x+ \frac{189}{ \color{blue}{99} })& = & (\frac{-297}{ \color{blue}{99} }x+ \frac{22}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 1386x \color{red}{+189} & = & \color{red}{-297x} +22 \\\Leftrightarrow & 1386x \color{red}{+189} \color{blue}{-189} \color{blue}{+297x} & = & \color{red}{-297x} +22 \color{blue}{+297x} \color{blue}{-189} \\\Leftrightarrow & 1386x+297x& = & 22-189 \\\Leftrightarrow & \color{red}{1683} x& = & -167 \\\Leftrightarrow & x = \frac{-167}{1683} & & \\ & V = \left\{ \frac{-167}{1683} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-5x+\frac{2}{7})& = & 7x+\frac{3}{7} \\\Leftrightarrow & -30x+\frac{12}{7}& = & 7x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{-210}{ \color{blue}{7} }x+ \frac{12}{ \color{blue}{7} })& = & (\frac{49}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & -210x \color{red}{+12} & = & \color{red}{49x} +3 \\\Leftrightarrow & -210x \color{red}{+12} \color{blue}{-12} \color{blue}{-49x} & = & \color{red}{49x} +3 \color{blue}{-49x} \color{blue}{-12} \\\Leftrightarrow & -210x-49x& = & 3-12 \\\Leftrightarrow & \color{red}{-259} x& = & -9 \\\Leftrightarrow & x = \frac{-9}{-259} & & \\\Leftrightarrow & x = \frac{9}{259} & & \\ & V = \left\{ \frac{9}{259} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x-\frac{5}{7})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -4x+\frac{10}{7}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{+90} & = & \color{red}{-567x} +56 \\\Leftrightarrow & -252x \color{red}{+90} \color{blue}{-90} \color{blue}{+567x} & = & \color{red}{-567x} +56 \color{blue}{+567x} \color{blue}{-90} \\\Leftrightarrow & -252x+567x& = & 56-90 \\\Leftrightarrow & \color{red}{315} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{315} & & \\ & V = \left\{ \frac{-34}{315} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{5}{7})& = & 5x+\frac{6}{5} \\\Leftrightarrow & -12x+\frac{30}{7}& = & 5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+150} & = & \color{red}{175x} +42 \\\Leftrightarrow & -420x \color{red}{+150} \color{blue}{-150} \color{blue}{-175x} & = & \color{red}{175x} +42 \color{blue}{-175x} \color{blue}{-150} \\\Leftrightarrow & -420x-175x& = & 42-150 \\\Leftrightarrow & \color{red}{-595} x& = & -108 \\\Leftrightarrow & x = \frac{-108}{-595} & & \\\Leftrightarrow & x = \frac{108}{595} & & \\ & V = \left\{ \frac{108}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{5}{3})& = & 9x+\frac{2}{7} \\\Leftrightarrow & -8x+\frac{20}{3}& = & 9x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+140} & = & \color{red}{189x} +6 \\\Leftrightarrow & -168x \color{red}{+140} \color{blue}{-140} \color{blue}{-189x} & = & \color{red}{189x} +6 \color{blue}{-189x} \color{blue}{-140} \\\Leftrightarrow & -168x-189x& = & 6-140 \\\Leftrightarrow & \color{red}{-357} x& = & -134 \\\Leftrightarrow & x = \frac{-134}{-357} & & \\\Leftrightarrow & x = \frac{134}{357} & & \\ & V = \left\{ \frac{134}{357} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-2x+\frac{3}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{12}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{36}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+36} & = & \color{red}{63x} +28 \\\Leftrightarrow & -168x \color{red}{+36} \color{blue}{-36} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{-36} \\\Leftrightarrow & -168x-63x& = & 28-36 \\\Leftrightarrow & \color{red}{-231} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-231} & & \\\Leftrightarrow & x = \frac{8}{231} & & \\ & V = \left\{ \frac{8}{231} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{11})& = & 7x+\frac{4}{7} \\\Leftrightarrow & -6x+\frac{10}{11}& = & 7x+\frac{4}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{70}{ \color{blue}{77} })& = & (\frac{539}{ \color{blue}{77} }x+ \frac{44}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+70} & = & \color{red}{539x} +44 \\\Leftrightarrow & -462x \color{red}{+70} \color{blue}{-70} \color{blue}{-539x} & = & \color{red}{539x} +44 \color{blue}{-539x} \color{blue}{-70} \\\Leftrightarrow & -462x-539x& = & 44-70 \\\Leftrightarrow & \color{red}{-1001} x& = & -26 \\\Leftrightarrow & x = \frac{-26}{-1001} & & \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{5})& = & -2x+\frac{10}{11} \\\Leftrightarrow & 21x-\frac{14}{5}& = & -2x+\frac{10}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{1155}{ \color{blue}{55} }x- \frac{154}{ \color{blue}{55} })& = & (\frac{-110}{ \color{blue}{55} }x+ \frac{50}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 1155x \color{red}{-154} & = & \color{red}{-110x} +50 \\\Leftrightarrow & 1155x \color{red}{-154} \color{blue}{+154} \color{blue}{+110x} & = & \color{red}{-110x} +50 \color{blue}{+110x} \color{blue}{+154} \\\Leftrightarrow & 1155x+110x& = & 50+154 \\\Leftrightarrow & \color{red}{1265} x& = & 204 \\\Leftrightarrow & x = \frac{204}{1265} & & \\ & V = \left\{ \frac{204}{1265} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x-\frac{4}{11})& = & 5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{16}{11}& = & 5x+\frac{8}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x+ \frac{80}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{88}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{+80} & = & \color{red}{275x} +88 \\\Leftrightarrow & 660x \color{red}{+80} \color{blue}{-80} \color{blue}{-275x} & = & \color{red}{275x} +88 \color{blue}{-275x} \color{blue}{-80} \\\Leftrightarrow & 660x-275x& = & 88-80 \\\Leftrightarrow & \color{red}{385} x& = & 8 \\\Leftrightarrow & x = \frac{8}{385} & & \\ & V = \left\{ \frac{8}{385} \right\} & \\\end{align}\)