Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (5x+\frac{3}{8})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -35x-\frac{21}{8}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-21} & = & \color{red}{-72x} +28 \\\Leftrightarrow & -280x \color{red}{-21} \color{blue}{+21} \color{blue}{+72x} & = & \color{red}{-72x} +28 \color{blue}{+72x} \color{blue}{+21} \\\Leftrightarrow & -280x+72x& = & 28+21 \\\Leftrightarrow & \color{red}{-208} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-208} & & \\\Leftrightarrow & x = \frac{-49}{208} & & \\ & V = \left\{ \frac{-49}{208} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x+\frac{4}{5})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 12x-\frac{12}{5}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x- \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{50}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{-36} & = & \color{red}{-75x} +50 \\\Leftrightarrow & 180x \color{red}{-36} \color{blue}{+36} \color{blue}{+75x} & = & \color{red}{-75x} +50 \color{blue}{+75x} \color{blue}{+36} \\\Leftrightarrow & 180x+75x& = & 50+36 \\\Leftrightarrow & \color{red}{255} x& = & 86 \\\Leftrightarrow & x = \frac{86}{255} & & \\ & V = \left\{ \frac{86}{255} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{11})& = & -7x+\frac{2}{11} \\\Leftrightarrow & 30x+\frac{30}{11}& = & -7x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{330}{ \color{blue}{11} }x+ \frac{30}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 330x \color{red}{+30} & = & \color{red}{-77x} +2 \\\Leftrightarrow & 330x \color{red}{+30} \color{blue}{-30} \color{blue}{+77x} & = & \color{red}{-77x} +2 \color{blue}{+77x} \color{blue}{-30} \\\Leftrightarrow & 330x+77x& = & 2-30 \\\Leftrightarrow & \color{red}{407} x& = & -28 \\\Leftrightarrow & x = \frac{-28}{407} & & \\ & V = \left\{ \frac{-28}{407} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x+\frac{2}{7})& = & 7x+\frac{3}{2} \\\Leftrightarrow & -6x-\frac{6}{7}& = & 7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-84}{ \color{blue}{14} }x- \frac{12}{ \color{blue}{14} })& = & (\frac{98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -84x \color{red}{-12} & = & \color{red}{98x} +21 \\\Leftrightarrow & -84x \color{red}{-12} \color{blue}{+12} \color{blue}{-98x} & = & \color{red}{98x} +21 \color{blue}{-98x} \color{blue}{+12} \\\Leftrightarrow & -84x-98x& = & 21+12 \\\Leftrightarrow & \color{red}{-182} x& = & 33 \\\Leftrightarrow & x = \frac{33}{-182} & & \\\Leftrightarrow & x = \frac{-33}{182} & & \\ & V = \left\{ \frac{-33}{182} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{4}{11})& = & 8x+\frac{9}{10} \\\Leftrightarrow & -21x-\frac{28}{11}& = & 8x+\frac{9}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-2310}{ \color{blue}{110} }x- \frac{280}{ \color{blue}{110} })& = & (\frac{880}{ \color{blue}{110} }x+ \frac{99}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -2310x \color{red}{-280} & = & \color{red}{880x} +99 \\\Leftrightarrow & -2310x \color{red}{-280} \color{blue}{+280} \color{blue}{-880x} & = & \color{red}{880x} +99 \color{blue}{-880x} \color{blue}{+280} \\\Leftrightarrow & -2310x-880x& = & 99+280 \\\Leftrightarrow & \color{red}{-3190} x& = & 379 \\\Leftrightarrow & x = \frac{379}{-3190} & & \\\Leftrightarrow & x = \frac{-379}{3190} & & \\ & V = \left\{ \frac{-379}{3190} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{2}{11})& = & 7x+\frac{4}{11} \\\Leftrightarrow & -6x+\frac{6}{11}& = & 7x+\frac{4}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-66}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} })& = & (\frac{77}{ \color{blue}{11} }x+ \frac{4}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -66x \color{red}{+6} & = & \color{red}{77x} +4 \\\Leftrightarrow & -66x \color{red}{+6} \color{blue}{-6} \color{blue}{-77x} & = & \color{red}{77x} +4 \color{blue}{-77x} \color{blue}{-6} \\\Leftrightarrow & -66x-77x& = & 4-6 \\\Leftrightarrow & \color{red}{-143} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{-143} & & \\\Leftrightarrow & x = \frac{2}{143} & & \\ & V = \left\{ \frac{2}{143} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x+\frac{2}{5})& = & 7x+\frac{8}{11} \\\Leftrightarrow & -6x-\frac{4}{5}& = & 7x+\frac{8}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-330}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{385}{ \color{blue}{55} }x+ \frac{40}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -330x \color{red}{-44} & = & \color{red}{385x} +40 \\\Leftrightarrow & -330x \color{red}{-44} \color{blue}{+44} \color{blue}{-385x} & = & \color{red}{385x} +40 \color{blue}{-385x} \color{blue}{+44} \\\Leftrightarrow & -330x-385x& = & 40+44 \\\Leftrightarrow & \color{red}{-715} x& = & 84 \\\Leftrightarrow & x = \frac{84}{-715} & & \\\Leftrightarrow & x = \frac{-84}{715} & & \\ & V = \left\{ \frac{-84}{715} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{2}{9})& = & 3x+\frac{2}{3} \\\Leftrightarrow & 8x+\frac{4}{9}& = & 3x+\frac{2}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{6}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+4} & = & \color{red}{27x} +6 \\\Leftrightarrow & 72x \color{red}{+4} \color{blue}{-4} \color{blue}{-27x} & = & \color{red}{27x} +6 \color{blue}{-27x} \color{blue}{-4} \\\Leftrightarrow & 72x-27x& = & 6-4 \\\Leftrightarrow & \color{red}{45} x& = & 2 \\\Leftrightarrow & x = \frac{2}{45} & & \\ & V = \left\{ \frac{2}{45} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{3}{11})& = & 5x+\frac{3}{5} \\\Leftrightarrow & 18x-\frac{18}{11}& = & 5x+\frac{3}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{33}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-90} & = & \color{red}{275x} +33 \\\Leftrightarrow & 990x \color{red}{-90} \color{blue}{+90} \color{blue}{-275x} & = & \color{red}{275x} +33 \color{blue}{-275x} \color{blue}{+90} \\\Leftrightarrow & 990x-275x& = & 33+90 \\\Leftrightarrow & \color{red}{715} x& = & 123 \\\Leftrightarrow & x = \frac{123}{715} & & \\ & V = \left\{ \frac{123}{715} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{7})& = & -9x+\frac{8}{11} \\\Leftrightarrow & -8x+\frac{20}{7}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-616}{ \color{blue}{77} }x+ \frac{220}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{56}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -616x \color{red}{+220} & = & \color{red}{-693x} +56 \\\Leftrightarrow & -616x \color{red}{+220} \color{blue}{-220} \color{blue}{+693x} & = & \color{red}{-693x} +56 \color{blue}{+693x} \color{blue}{-220} \\\Leftrightarrow & -616x+693x& = & 56-220 \\\Leftrightarrow & \color{red}{77} x& = & -164 \\\Leftrightarrow & x = \frac{-164}{77} & & \\ & V = \left\{ \frac{-164}{77} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{4}{9})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 10x-\frac{8}{9}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{90}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 90x \color{red}{-8} & = & \color{red}{81x} +8 \\\Leftrightarrow & 90x \color{red}{-8} \color{blue}{+8} \color{blue}{-81x} & = & \color{red}{81x} +8 \color{blue}{-81x} \color{blue}{+8} \\\Leftrightarrow & 90x-81x& = & 8+8 \\\Leftrightarrow & \color{red}{9} x& = & 16 \\\Leftrightarrow & x = \frac{16}{9} & & \\ & V = \left\{ \frac{16}{9} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-\frac{4}{3})& = & -8x+\frac{8}{5} \\\Leftrightarrow & -15x+\frac{20}{3}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 3 en 5 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-225}{ \color{blue}{15} }x+ \frac{100}{ \color{blue}{15} })& = & (\frac{-120}{ \color{blue}{15} }x+ \frac{24}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -225x \color{red}{+100} & = & \color{red}{-120x} +24 \\\Leftrightarrow & -225x \color{red}{+100} \color{blue}{-100} \color{blue}{+120x} & = & \color{red}{-120x} +24 \color{blue}{+120x} \color{blue}{-100} \\\Leftrightarrow & -225x+120x& = & 24-100 \\\Leftrightarrow & \color{red}{-105} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{-105} & & \\\Leftrightarrow & x = \frac{76}{105} & & \\ & V = \left\{ \frac{76}{105} \right\} & \\\end{align}\)