Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{7})& = & -4x+\frac{3}{7} \\\Leftrightarrow & 9x+\frac{15}{7}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{63}{ \color{blue}{7} }x+ \frac{15}{ \color{blue}{7} })& = & (\frac{-28}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 63x \color{red}{+15} & = & \color{red}{-28x} +3 \\\Leftrightarrow & 63x \color{red}{+15} \color{blue}{-15} \color{blue}{+28x} & = & \color{red}{-28x} +3 \color{blue}{+28x} \color{blue}{-15} \\\Leftrightarrow & 63x+28x& = & 3-15 \\\Leftrightarrow & \color{red}{91} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{91} & & \\ & V = \left\{ \frac{-12}{91} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x-\frac{5}{2})& = & -4x+\frac{3}{7} \\\Leftrightarrow & -15x-\frac{25}{2}& = & -4x+\frac{3}{7} \\ & & & \text{kgv van noemers 2 en 7 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-210}{ \color{blue}{14} }x- \frac{175}{ \color{blue}{14} })& = & (\frac{-56}{ \color{blue}{14} }x+ \frac{6}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -210x \color{red}{-175} & = & \color{red}{-56x} +6 \\\Leftrightarrow & -210x \color{red}{-175} \color{blue}{+175} \color{blue}{+56x} & = & \color{red}{-56x} +6 \color{blue}{+56x} \color{blue}{+175} \\\Leftrightarrow & -210x+56x& = & 6+175 \\\Leftrightarrow & \color{red}{-154} x& = & 181 \\\Leftrightarrow & x = \frac{181}{-154} & & \\\Leftrightarrow & x = \frac{-181}{154} & & \\ & V = \left\{ \frac{-181}{154} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x-\frac{5}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{30}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{660}{ \color{blue}{55} }x- \frac{150}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 660x \color{red}{-150} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 660x \color{red}{-150} \color{blue}{+150} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+150} \\\Leftrightarrow & 660x+275x& = & 66+150 \\\Leftrightarrow & \color{red}{935} x& = & 216 \\\Leftrightarrow & x = \frac{216}{935} & & \\ & V = \left\{ \frac{216}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{3}{7})& = & -5x+\frac{9}{11} \\\Leftrightarrow & -12x+\frac{9}{7}& = & -5x+\frac{9}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-924}{ \color{blue}{77} }x+ \frac{99}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{63}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -924x \color{red}{+99} & = & \color{red}{-385x} +63 \\\Leftrightarrow & -924x \color{red}{+99} \color{blue}{-99} \color{blue}{+385x} & = & \color{red}{-385x} +63 \color{blue}{+385x} \color{blue}{-99} \\\Leftrightarrow & -924x+385x& = & 63-99 \\\Leftrightarrow & \color{red}{-539} x& = & -36 \\\Leftrightarrow & x = \frac{-36}{-539} & & \\\Leftrightarrow & x = \frac{36}{539} & & \\ & V = \left\{ \frac{36}{539} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{2}{7})& = & -9x+\frac{4}{11} \\\Leftrightarrow & -8x-\frac{4}{7}& = & -9x+\frac{4}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x- \frac{44}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{28}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{-44} & = & \color{red}{-693x} +28 \\\Leftrightarrow & -616x \color{red}{-44} \color{blue}{+44} \color{blue}{+693x} & = & \color{red}{-693x} +28 \color{blue}{+693x} \color{blue}{+44} \\\Leftrightarrow & -616x+693x& = & 28+44 \\\Leftrightarrow & \color{red}{77} x& = & 72 \\\Leftrightarrow & x = \frac{72}{77} & & \\ & V = \left\{ \frac{72}{77} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{4}{9})& = & 8x+\frac{7}{4} \\\Leftrightarrow & 35x+\frac{28}{9}& = & 8x+\frac{7}{4} \\ & & & \text{kgv van noemers 9 en 4 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{1260}{ \color{blue}{36} }x+ \frac{112}{ \color{blue}{36} })& = & (\frac{288}{ \color{blue}{36} }x+ \frac{63}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & 1260x \color{red}{+112} & = & \color{red}{288x} +63 \\\Leftrightarrow & 1260x \color{red}{+112} \color{blue}{-112} \color{blue}{-288x} & = & \color{red}{288x} +63 \color{blue}{-288x} \color{blue}{-112} \\\Leftrightarrow & 1260x-288x& = & 63-112 \\\Leftrightarrow & \color{red}{972} x& = & -49 \\\Leftrightarrow & x = \frac{-49}{972} & & \\ & V = \left\{ \frac{-49}{972} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{2}{11})& = & 5x+\frac{8}{9} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1188}{ \color{blue}{99} }x- \frac{108}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1188x \color{red}{-108} & = & \color{red}{495x} +88 \\\Leftrightarrow & -1188x \color{red}{-108} \color{blue}{+108} \color{blue}{-495x} & = & \color{red}{495x} +88 \color{blue}{-495x} \color{blue}{+108} \\\Leftrightarrow & -1188x-495x& = & 88+108 \\\Leftrightarrow & \color{red}{-1683} x& = & 196 \\\Leftrightarrow & x = \frac{196}{-1683} & & \\\Leftrightarrow & x = \frac{-196}{1683} & & \\ & V = \left\{ \frac{-196}{1683} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{11})& = & -3x+\frac{9}{10} \\\Leftrightarrow & 28x-\frac{35}{11}& = & -3x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{3080}{ \color{blue}{110} }x- \frac{350}{ \color{blue}{110} })& = & (\frac{-330}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & 3080x \color{red}{-350} & = & \color{red}{-330x} +99 \\\Leftrightarrow & 3080x \color{red}{-350} \color{blue}{+350} \color{blue}{+330x} & = & \color{red}{-330x} +99 \color{blue}{+330x} \color{blue}{+350} \\\Leftrightarrow & 3080x+330x& = & 99+350 \\\Leftrightarrow & \color{red}{3410} x& = & 449 \\\Leftrightarrow & x = \frac{449}{3410} & & \\ & V = \left\{ \frac{449}{3410} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (2x+\frac{4}{7})& = & -7x+\frac{10}{7} \\\Leftrightarrow & 4x+\frac{8}{7}& = & -7x+\frac{10}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{8}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{10}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+8} & = & \color{red}{-49x} +10 \\\Leftrightarrow & 28x \color{red}{+8} \color{blue}{-8} \color{blue}{+49x} & = & \color{red}{-49x} +10 \color{blue}{+49x} \color{blue}{-8} \\\Leftrightarrow & 28x+49x& = & 10-8 \\\Leftrightarrow & \color{red}{77} x& = & 2 \\\Leftrightarrow & x = \frac{2}{77} & & \\ & V = \left\{ \frac{2}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 4x+\frac{8}{5} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 4x+\frac{8}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{32}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 500x \color{red}{-75} & = & \color{red}{80x} +32 \\\Leftrightarrow & 500x \color{red}{-75} \color{blue}{+75} \color{blue}{-80x} & = & \color{red}{80x} +32 \color{blue}{-80x} \color{blue}{+75} \\\Leftrightarrow & 500x-80x& = & 32+75 \\\Leftrightarrow & \color{red}{420} x& = & 107 \\\Leftrightarrow & x = \frac{107}{420} & & \\ & V = \left\{ \frac{107}{420} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{5}{11})& = & -9x+\frac{5}{7} \\\Leftrightarrow & -25x-\frac{25}{11}& = & -9x+\frac{5}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1925}{ \color{blue}{77} }x- \frac{175}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{55}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1925x \color{red}{-175} & = & \color{red}{-693x} +55 \\\Leftrightarrow & -1925x \color{red}{-175} \color{blue}{+175} \color{blue}{+693x} & = & \color{red}{-693x} +55 \color{blue}{+693x} \color{blue}{+175} \\\Leftrightarrow & -1925x+693x& = & 55+175 \\\Leftrightarrow & \color{red}{-1232} x& = & 230 \\\Leftrightarrow & x = \frac{230}{-1232} & & \\\Leftrightarrow & x = \frac{-115}{616} & & \\ & V = \left\{ \frac{-115}{616} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{5}{11})& = & 7x+\frac{3}{2} \\\Leftrightarrow & 30x-\frac{30}{11}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{660}{ \color{blue}{22} }x- \frac{60}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 660x \color{red}{-60} & = & \color{red}{154x} +33 \\\Leftrightarrow & 660x \color{red}{-60} \color{blue}{+60} \color{blue}{-154x} & = & \color{red}{154x} +33 \color{blue}{-154x} \color{blue}{+60} \\\Leftrightarrow & 660x-154x& = & 33+60 \\\Leftrightarrow & \color{red}{506} x& = & 93 \\\Leftrightarrow & x = \frac{93}{506} & & \\ & V = \left\{ \frac{93}{506} \right\} & \\\end{align}\)