Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{5}{4})& = & 5x+\frac{3}{11} \\\Leftrightarrow & 6x-\frac{15}{4}& = & 5x+\frac{3}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{264}{ \color{blue}{44} }x- \frac{165}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{12}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 264x \color{red}{-165} & = & \color{red}{220x} +12 \\\Leftrightarrow & 264x \color{red}{-165} \color{blue}{+165} \color{blue}{-220x} & = & \color{red}{220x} +12 \color{blue}{-220x} \color{blue}{+165} \\\Leftrightarrow & 264x-220x& = & 12+165 \\\Leftrightarrow & \color{red}{44} x& = & 177 \\\Leftrightarrow & x = \frac{177}{44} & & \\ & V = \left\{ \frac{177}{44} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (3x-\frac{5}{8})& = & -5x+\frac{7}{11} \\\Leftrightarrow & -9x+\frac{15}{8}& = & -5x+\frac{7}{11} \\ & & & \text{kgv van noemers 8 en 11 is 88} \\\Leftrightarrow & \color{blue}{88} .(\frac{-792}{ \color{blue}{88} }x+ \frac{165}{ \color{blue}{88} })& = & (\frac{-440}{ \color{blue}{88} }x+ \frac{56}{ \color{blue}{88} }). \color{blue}{88} \\\Leftrightarrow & -792x \color{red}{+165} & = & \color{red}{-440x} +56 \\\Leftrightarrow & -792x \color{red}{+165} \color{blue}{-165} \color{blue}{+440x} & = & \color{red}{-440x} +56 \color{blue}{+440x} \color{blue}{-165} \\\Leftrightarrow & -792x+440x& = & 56-165 \\\Leftrightarrow & \color{red}{-352} x& = & -109 \\\Leftrightarrow & x = \frac{-109}{-352} & & \\\Leftrightarrow & x = \frac{109}{352} & & \\ & V = \left\{ \frac{109}{352} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{5}{7})& = & 7x+\frac{8}{5} \\\Leftrightarrow & 16x-\frac{20}{7}& = & 7x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{560}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{245}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 560x \color{red}{-100} & = & \color{red}{245x} +56 \\\Leftrightarrow & 560x \color{red}{-100} \color{blue}{+100} \color{blue}{-245x} & = & \color{red}{245x} +56 \color{blue}{-245x} \color{blue}{+100} \\\Leftrightarrow & 560x-245x& = & 56+100 \\\Leftrightarrow & \color{red}{315} x& = & 156 \\\Leftrightarrow & x = \frac{156}{315} & & \\\Leftrightarrow & x = \frac{52}{105} & & \\ & V = \left\{ \frac{52}{105} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-4x+\frac{3}{11})& = & 7x+\frac{2}{3} \\\Leftrightarrow & 24x-\frac{18}{11}& = & 7x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{792}{ \color{blue}{33} }x- \frac{54}{ \color{blue}{33} })& = & (\frac{231}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 792x \color{red}{-54} & = & \color{red}{231x} +22 \\\Leftrightarrow & 792x \color{red}{-54} \color{blue}{+54} \color{blue}{-231x} & = & \color{red}{231x} +22 \color{blue}{-231x} \color{blue}{+54} \\\Leftrightarrow & 792x-231x& = & 22+54 \\\Leftrightarrow & \color{red}{561} x& = & 76 \\\Leftrightarrow & x = \frac{76}{561} & & \\ & V = \left\{ \frac{76}{561} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x-\frac{3}{7})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 12x-\frac{9}{7}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x- \frac{45}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{-45} & = & \color{red}{-175x} +42 \\\Leftrightarrow & 420x \color{red}{-45} \color{blue}{+45} \color{blue}{+175x} & = & \color{red}{-175x} +42 \color{blue}{+175x} \color{blue}{+45} \\\Leftrightarrow & 420x+175x& = & 42+45 \\\Leftrightarrow & \color{red}{595} x& = & 87 \\\Leftrightarrow & x = \frac{87}{595} & & \\ & V = \left\{ \frac{87}{595} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x+\frac{4}{3})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 20x+\frac{20}{3}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{420}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 420x \color{red}{+140} & = & \color{red}{63x} +30 \\\Leftrightarrow & 420x \color{red}{+140} \color{blue}{-140} \color{blue}{-63x} & = & \color{red}{63x} +30 \color{blue}{-63x} \color{blue}{-140} \\\Leftrightarrow & 420x-63x& = & 30-140 \\\Leftrightarrow & \color{red}{357} x& = & -110 \\\Leftrightarrow & x = \frac{-110}{357} & & \\ & V = \left\{ \frac{-110}{357} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -9x+\frac{5}{11} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -9x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+220} & = & \color{red}{-297x} +15 \\\Leftrightarrow & -264x \color{red}{+220} \color{blue}{-220} \color{blue}{+297x} & = & \color{red}{-297x} +15 \color{blue}{+297x} \color{blue}{-220} \\\Leftrightarrow & -264x+297x& = & 15-220 \\\Leftrightarrow & \color{red}{33} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{33} & & \\ & V = \left\{ \frac{-205}{33} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{3}{7})& = & -3x+\frac{8}{3} \\\Leftrightarrow & -8x+\frac{6}{7}& = & -3x+\frac{8}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{56}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{+18} & = & \color{red}{-63x} +56 \\\Leftrightarrow & -168x \color{red}{+18} \color{blue}{-18} \color{blue}{+63x} & = & \color{red}{-63x} +56 \color{blue}{+63x} \color{blue}{-18} \\\Leftrightarrow & -168x+63x& = & 56-18 \\\Leftrightarrow & \color{red}{-105} x& = & 38 \\\Leftrightarrow & x = \frac{38}{-105} & & \\\Leftrightarrow & x = \frac{-38}{105} & & \\ & V = \left\{ \frac{-38}{105} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-462}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -462x \color{red}{+110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & -462x \color{red}{+110} \color{blue}{-110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{-110} \\\Leftrightarrow & -462x+539x& = & 42-110 \\\Leftrightarrow & \color{red}{77} x& = & -68 \\\Leftrightarrow & x = \frac{-68}{77} & & \\ & V = \left\{ \frac{-68}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x-\frac{3}{5})& = & 7x+\frac{7}{6} \\\Leftrightarrow & -10x-\frac{6}{5}& = & 7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-300}{ \color{blue}{30} }x- \frac{36}{ \color{blue}{30} })& = & (\frac{210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -300x \color{red}{-36} & = & \color{red}{210x} +35 \\\Leftrightarrow & -300x \color{red}{-36} \color{blue}{+36} \color{blue}{-210x} & = & \color{red}{210x} +35 \color{blue}{-210x} \color{blue}{+36} \\\Leftrightarrow & -300x-210x& = & 35+36 \\\Leftrightarrow & \color{red}{-510} x& = & 71 \\\Leftrightarrow & x = \frac{71}{-510} & & \\\Leftrightarrow & x = \frac{-71}{510} & & \\ & V = \left\{ \frac{-71}{510} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -9x+\frac{3}{10} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -9x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{280}{ \color{blue}{70} }x+ \frac{60}{ \color{blue}{70} })& = & (\frac{-630}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & 280x \color{red}{+60} & = & \color{red}{-630x} +21 \\\Leftrightarrow & 280x \color{red}{+60} \color{blue}{-60} \color{blue}{+630x} & = & \color{red}{-630x} +21 \color{blue}{+630x} \color{blue}{-60} \\\Leftrightarrow & 280x+630x& = & 21-60 \\\Leftrightarrow & \color{red}{910} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{910} & & \\\Leftrightarrow & x = \frac{-3}{70} & & \\ & V = \left\{ \frac{-3}{70} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x+\frac{4}{5})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -12x-\frac{12}{5}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{50}{ \color{blue}{10} }x+ \frac{35}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{-24} & = & \color{red}{50x} +35 \\\Leftrightarrow & -120x \color{red}{-24} \color{blue}{+24} \color{blue}{-50x} & = & \color{red}{50x} +35 \color{blue}{-50x} \color{blue}{+24} \\\Leftrightarrow & -120x-50x& = & 35+24 \\\Leftrightarrow & \color{red}{-170} x& = & 59 \\\Leftrightarrow & x = \frac{59}{-170} & & \\\Leftrightarrow & x = \frac{-59}{170} & & \\ & V = \left\{ \frac{-59}{170} \right\} & \\\end{align}\)