Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{3}{5})& = & 7x+\frac{7}{12} \\\Leftrightarrow & -6x+\frac{9}{5}& = & 7x+\frac{7}{12} \\ & & & \text{kgv van noemers 5 en 12 is 60} \\\Leftrightarrow & \color{blue}{60} .(\frac{-360}{ \color{blue}{60} }x+ \frac{108}{ \color{blue}{60} })& = & (\frac{420}{ \color{blue}{60} }x+ \frac{35}{ \color{blue}{60} }). \color{blue}{60} \\\Leftrightarrow & -360x \color{red}{+108} & = & \color{red}{420x} +35 \\\Leftrightarrow & -360x \color{red}{+108} \color{blue}{-108} \color{blue}{-420x} & = & \color{red}{420x} +35 \color{blue}{-420x} \color{blue}{-108} \\\Leftrightarrow & -360x-420x& = & 35-108 \\\Leftrightarrow & \color{red}{-780} x& = & -73 \\\Leftrightarrow & x = \frac{-73}{-780} & & \\\Leftrightarrow & x = \frac{73}{780} & & \\ & V = \left\{ \frac{73}{780} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (5x+\frac{3}{8})& = & -9x+\frac{9}{4} \\\Leftrightarrow & 35x+\frac{21}{8}& = & -9x+\frac{9}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{280}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{18}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 280x \color{red}{+21} & = & \color{red}{-72x} +18 \\\Leftrightarrow & 280x \color{red}{+21} \color{blue}{-21} \color{blue}{+72x} & = & \color{red}{-72x} +18 \color{blue}{+72x} \color{blue}{-21} \\\Leftrightarrow & 280x+72x& = & 18-21 \\\Leftrightarrow & \color{red}{352} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{352} & & \\ & V = \left\{ \frac{-3}{352} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x+\frac{2}{7})& = & 4x+\frac{10}{3} \\\Leftrightarrow & -15x-\frac{10}{7}& = & 4x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-315}{ \color{blue}{21} }x- \frac{30}{ \color{blue}{21} })& = & (\frac{84}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -315x \color{red}{-30} & = & \color{red}{84x} +70 \\\Leftrightarrow & -315x \color{red}{-30} \color{blue}{+30} \color{blue}{-84x} & = & \color{red}{84x} +70 \color{blue}{-84x} \color{blue}{+30} \\\Leftrightarrow & -315x-84x& = & 70+30 \\\Leftrightarrow & \color{red}{-399} x& = & 100 \\\Leftrightarrow & x = \frac{100}{-399} & & \\\Leftrightarrow & x = \frac{-100}{399} & & \\ & V = \left\{ \frac{-100}{399} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{5}{3})& = & -5x+\frac{5}{6} \\\Leftrightarrow & 12x-\frac{20}{3}& = & -5x+\frac{5}{6} \\ & & & \text{kgv van noemers 3 en 6 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{72}{ \color{blue}{6} }x- \frac{40}{ \color{blue}{6} })& = & (\frac{-30}{ \color{blue}{6} }x+ \frac{5}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 72x \color{red}{-40} & = & \color{red}{-30x} +5 \\\Leftrightarrow & 72x \color{red}{-40} \color{blue}{+40} \color{blue}{+30x} & = & \color{red}{-30x} +5 \color{blue}{+30x} \color{blue}{+40} \\\Leftrightarrow & 72x+30x& = & 5+40 \\\Leftrightarrow & \color{red}{102} x& = & 45 \\\Leftrightarrow & x = \frac{45}{102} & & \\\Leftrightarrow & x = \frac{15}{34} & & \\ & V = \left\{ \frac{15}{34} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{3})& = & -7x+\frac{8}{3} \\\Leftrightarrow & -16x+\frac{16}{3}& = & -7x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-48}{ \color{blue}{3} }x+ \frac{16}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -48x \color{red}{+16} & = & \color{red}{-21x} +8 \\\Leftrightarrow & -48x \color{red}{+16} \color{blue}{-16} \color{blue}{+21x} & = & \color{red}{-21x} +8 \color{blue}{+21x} \color{blue}{-16} \\\Leftrightarrow & -48x+21x& = & 8-16 \\\Leftrightarrow & \color{red}{-27} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-27} & & \\\Leftrightarrow & x = \frac{8}{27} & & \\ & V = \left\{ \frac{8}{27} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x+\frac{3}{5})& = & -9x+\frac{6}{7} \\\Leftrightarrow & 8x-\frac{12}{5}& = & -9x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{-315}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-84} & = & \color{red}{-315x} +30 \\\Leftrightarrow & 280x \color{red}{-84} \color{blue}{+84} \color{blue}{+315x} & = & \color{red}{-315x} +30 \color{blue}{+315x} \color{blue}{+84} \\\Leftrightarrow & 280x+315x& = & 30+84 \\\Leftrightarrow & \color{red}{595} x& = & 114 \\\Leftrightarrow & x = \frac{114}{595} & & \\ & V = \left\{ \frac{114}{595} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-3x+\frac{5}{7})& = & 5x+\frac{6}{11} \\\Leftrightarrow & 12x-\frac{20}{7}& = & 5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{924}{ \color{blue}{77} }x- \frac{220}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 924x \color{red}{-220} & = & \color{red}{385x} +42 \\\Leftrightarrow & 924x \color{red}{-220} \color{blue}{+220} \color{blue}{-385x} & = & \color{red}{385x} +42 \color{blue}{-385x} \color{blue}{+220} \\\Leftrightarrow & 924x-385x& = & 42+220 \\\Leftrightarrow & \color{red}{539} x& = & 262 \\\Leftrightarrow & x = \frac{262}{539} & & \\ & V = \left\{ \frac{262}{539} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{3}{7})& = & -8x+\frac{6}{5} \\\Leftrightarrow & 15x+\frac{9}{7}& = & -8x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{45}{ \color{blue}{35} })& = & (\frac{-280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+45} & = & \color{red}{-280x} +42 \\\Leftrightarrow & 525x \color{red}{+45} \color{blue}{-45} \color{blue}{+280x} & = & \color{red}{-280x} +42 \color{blue}{+280x} \color{blue}{-45} \\\Leftrightarrow & 525x+280x& = & 42-45 \\\Leftrightarrow & \color{red}{805} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{805} & & \\ & V = \left\{ \frac{-3}{805} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x+\frac{4}{5})& = & 2x+\frac{5}{6} \\\Leftrightarrow & 15x+\frac{12}{5}& = & 2x+\frac{5}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{450}{ \color{blue}{30} }x+ \frac{72}{ \color{blue}{30} })& = & (\frac{60}{ \color{blue}{30} }x+ \frac{25}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{+72} & = & \color{red}{60x} +25 \\\Leftrightarrow & 450x \color{red}{+72} \color{blue}{-72} \color{blue}{-60x} & = & \color{red}{60x} +25 \color{blue}{-60x} \color{blue}{-72} \\\Leftrightarrow & 450x-60x& = & 25-72 \\\Leftrightarrow & \color{red}{390} x& = & -47 \\\Leftrightarrow & x = \frac{-47}{390} & & \\ & V = \left\{ \frac{-47}{390} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x-\frac{4}{5})& = & -7x+\frac{5}{3} \\\Leftrightarrow & -6x-\frac{8}{5}& = & -7x+\frac{5}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-90}{ \color{blue}{15} }x- \frac{24}{ \color{blue}{15} })& = & (\frac{-105}{ \color{blue}{15} }x+ \frac{25}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -90x \color{red}{-24} & = & \color{red}{-105x} +25 \\\Leftrightarrow & -90x \color{red}{-24} \color{blue}{+24} \color{blue}{+105x} & = & \color{red}{-105x} +25 \color{blue}{+105x} \color{blue}{+24} \\\Leftrightarrow & -90x+105x& = & 25+24 \\\Leftrightarrow & \color{red}{15} x& = & 49 \\\Leftrightarrow & x = \frac{49}{15} & & \\ & V = \left\{ \frac{49}{15} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{5}{12})& = & 2x+\frac{6}{11} \\\Leftrightarrow & -25x+\frac{25}{12}& = & 2x+\frac{6}{11} \\ & & & \text{kgv van noemers 12 en 11 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-3300}{ \color{blue}{132} }x+ \frac{275}{ \color{blue}{132} })& = & (\frac{264}{ \color{blue}{132} }x+ \frac{72}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -3300x \color{red}{+275} & = & \color{red}{264x} +72 \\\Leftrightarrow & -3300x \color{red}{+275} \color{blue}{-275} \color{blue}{-264x} & = & \color{red}{264x} +72 \color{blue}{-264x} \color{blue}{-275} \\\Leftrightarrow & -3300x-264x& = & 72-275 \\\Leftrightarrow & \color{red}{-3564} x& = & -203 \\\Leftrightarrow & x = \frac{-203}{-3564} & & \\\Leftrightarrow & x = \frac{203}{3564} & & \\ & V = \left\{ \frac{203}{3564} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{4}{11})& = & 5x+\frac{9}{2} \\\Leftrightarrow & -24x+\frac{24}{11}& = & 5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-528}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -528x \color{red}{+48} & = & \color{red}{110x} +99 \\\Leftrightarrow & -528x \color{red}{+48} \color{blue}{-48} \color{blue}{-110x} & = & \color{red}{110x} +99 \color{blue}{-110x} \color{blue}{-48} \\\Leftrightarrow & -528x-110x& = & 99-48 \\\Leftrightarrow & \color{red}{-638} x& = & 51 \\\Leftrightarrow & x = \frac{51}{-638} & & \\\Leftrightarrow & x = \frac{-51}{638} & & \\ & V = \left\{ \frac{-51}{638} \right\} & \\\end{align}\)