Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x-\frac{3}{4})& = & 3x+\frac{6}{5} \\\Leftrightarrow & 20x+\frac{15}{4}& = & 3x+\frac{6}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x+ \frac{75}{ \color{blue}{20} })& = & (\frac{60}{ \color{blue}{20} }x+ \frac{24}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{+75} & = & \color{red}{60x} +24 \\\Leftrightarrow & 400x \color{red}{+75} \color{blue}{-75} \color{blue}{-60x} & = & \color{red}{60x} +24 \color{blue}{-60x} \color{blue}{-75} \\\Leftrightarrow & 400x-60x& = & 24-75 \\\Leftrightarrow & \color{red}{340} x& = & -51 \\\Leftrightarrow & x = \frac{-51}{340} & & \\\Leftrightarrow & x = \frac{-3}{20} & & \\ & V = \left\{ \frac{-3}{20} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{5}{3})& = & 9x+\frac{4}{3} \\\Leftrightarrow & 20x-\frac{25}{3}& = & 9x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x- \frac{25}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{-25} & = & \color{red}{27x} +4 \\\Leftrightarrow & 60x \color{red}{-25} \color{blue}{+25} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{+25} \\\Leftrightarrow & 60x-27x& = & 4+25 \\\Leftrightarrow & \color{red}{33} x& = & 29 \\\Leftrightarrow & x = \frac{29}{33} & & \\ & V = \left\{ \frac{29}{33} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{4}{11})& = & -3x+\frac{3}{11} \\\Leftrightarrow & 4x-\frac{8}{11}& = & -3x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{44}{ \color{blue}{11} }x- \frac{8}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 44x \color{red}{-8} & = & \color{red}{-33x} +3 \\\Leftrightarrow & 44x \color{red}{-8} \color{blue}{+8} \color{blue}{+33x} & = & \color{red}{-33x} +3 \color{blue}{+33x} \color{blue}{+8} \\\Leftrightarrow & 44x+33x& = & 3+8 \\\Leftrightarrow & \color{red}{77} x& = & 11 \\\Leftrightarrow & x = \frac{11}{77} & & \\\Leftrightarrow & x = \frac{1}{7} & & \\ & V = \left\{ \frac{1}{7} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{2}{7})& = & -4x+\frac{8}{5} \\\Leftrightarrow & 15x+\frac{6}{7}& = & -4x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{525}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} })& = & (\frac{-140}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-140x} +56 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+140x} & = & \color{red}{-140x} +56 \color{blue}{+140x} \color{blue}{-30} \\\Leftrightarrow & 525x+140x& = & 56-30 \\\Leftrightarrow & \color{red}{665} x& = & 26 \\\Leftrightarrow & x = \frac{26}{665} & & \\ & V = \left\{ \frac{26}{665} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{3}{7})& = & -9x+\frac{5}{4} \\\Leftrightarrow & -8x-\frac{6}{7}& = & -9x+\frac{5}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-224}{ \color{blue}{28} }x- \frac{24}{ \color{blue}{28} })& = & (\frac{-252}{ \color{blue}{28} }x+ \frac{35}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -224x \color{red}{-24} & = & \color{red}{-252x} +35 \\\Leftrightarrow & -224x \color{red}{-24} \color{blue}{+24} \color{blue}{+252x} & = & \color{red}{-252x} +35 \color{blue}{+252x} \color{blue}{+24} \\\Leftrightarrow & -224x+252x& = & 35+24 \\\Leftrightarrow & \color{red}{28} x& = & 59 \\\Leftrightarrow & x = \frac{59}{28} & & \\ & V = \left\{ \frac{59}{28} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{2}{11})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -10x-\frac{10}{11}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x- \frac{40}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{-40} & = & \color{red}{-308x} +77 \\\Leftrightarrow & -440x \color{red}{-40} \color{blue}{+40} \color{blue}{+308x} & = & \color{red}{-308x} +77 \color{blue}{+308x} \color{blue}{+40} \\\Leftrightarrow & -440x+308x& = & 77+40 \\\Leftrightarrow & \color{red}{-132} x& = & 117 \\\Leftrightarrow & x = \frac{117}{-132} & & \\\Leftrightarrow & x = \frac{-39}{44} & & \\ & V = \left\{ \frac{-39}{44} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -5x+\frac{4}{5} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+150} & = & \color{red}{-175x} +28 \\\Leftrightarrow & 420x \color{red}{+150} \color{blue}{-150} \color{blue}{+175x} & = & \color{red}{-175x} +28 \color{blue}{+175x} \color{blue}{-150} \\\Leftrightarrow & 420x+175x& = & 28-150 \\\Leftrightarrow & \color{red}{595} x& = & -122 \\\Leftrightarrow & x = \frac{-122}{595} & & \\ & V = \left\{ \frac{-122}{595} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (3x-\frac{5}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{10}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+30} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{+30} \color{blue}{-30} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-30} \\\Leftrightarrow & -126x+147x& = & 28-30 \\\Leftrightarrow & \color{red}{21} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{21} & & \\ & V = \left\{ \frac{-2}{21} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{5}{7})& = & -2x+\frac{6}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & -2x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{-70}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{-70x} +42 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{+70x} & = & \color{red}{-70x} +42 \color{blue}{+70x} \color{blue}{+150} \\\Leftrightarrow & -630x+70x& = & 42+150 \\\Leftrightarrow & \color{red}{-560} x& = & 192 \\\Leftrightarrow & x = \frac{192}{-560} & & \\\Leftrightarrow & x = \frac{-12}{35} & & \\ & V = \left\{ \frac{-12}{35} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x+\frac{2}{3})& = & 9x+\frac{7}{3} \\\Leftrightarrow & 20x+\frac{8}{3}& = & 9x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{60}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 60x \color{red}{+8} & = & \color{red}{27x} +7 \\\Leftrightarrow & 60x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +7 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & 60x-27x& = & 7-8 \\\Leftrightarrow & \color{red}{33} x& = & -1 \\\Leftrightarrow & x = \frac{-1}{33} & & \\ & V = \left\{ \frac{-1}{33} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x-\frac{2}{11})& = & -3x+\frac{6}{11} \\\Leftrightarrow & -25x+\frac{10}{11}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-275}{ \color{blue}{11} }x+ \frac{10}{ \color{blue}{11} })& = & (\frac{-33}{ \color{blue}{11} }x+ \frac{6}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -275x \color{red}{+10} & = & \color{red}{-33x} +6 \\\Leftrightarrow & -275x \color{red}{+10} \color{blue}{-10} \color{blue}{+33x} & = & \color{red}{-33x} +6 \color{blue}{+33x} \color{blue}{-10} \\\Leftrightarrow & -275x+33x& = & 6-10 \\\Leftrightarrow & \color{red}{-242} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-242} & & \\\Leftrightarrow & x = \frac{2}{121} & & \\ & V = \left\{ \frac{2}{121} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & -5x+\frac{2}{11} \\\Leftrightarrow & -24x+\frac{18}{11}& = & -5x+\frac{2}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{-264}{ \color{blue}{11} }x+ \frac{18}{ \color{blue}{11} })& = & (\frac{-55}{ \color{blue}{11} }x+ \frac{2}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{-55x} +2 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{+55x} & = & \color{red}{-55x} +2 \color{blue}{+55x} \color{blue}{-18} \\\Leftrightarrow & -264x+55x& = & 2-18 \\\Leftrightarrow & \color{red}{-209} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-209} & & \\\Leftrightarrow & x = \frac{16}{209} & & \\ & V = \left\{ \frac{16}{209} \right\} & \\\end{align}\)