Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{4}{11})& = & -5x+\frac{4}{3} \\\Leftrightarrow & -12x+\frac{16}{11}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-396}{ \color{blue}{33} }x+ \frac{48}{ \color{blue}{33} })& = & (\frac{-165}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -396x \color{red}{+48} & = & \color{red}{-165x} +44 \\\Leftrightarrow & -396x \color{red}{+48} \color{blue}{-48} \color{blue}{+165x} & = & \color{red}{-165x} +44 \color{blue}{+165x} \color{blue}{-48} \\\Leftrightarrow & -396x+165x& = & 44-48 \\\Leftrightarrow & \color{red}{-231} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{-231} & & \\\Leftrightarrow & x = \frac{4}{231} & & \\ & V = \left\{ \frac{4}{231} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -5x+\frac{10}{3} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -5x+\frac{10}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{168}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} })& = & (\frac{-105}{ \color{blue}{21} }x+ \frac{70}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{-105x} +70 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{+105x} & = & \color{red}{-105x} +70 \color{blue}{+105x} \color{blue}{-18} \\\Leftrightarrow & 168x+105x& = & 70-18 \\\Leftrightarrow & \color{red}{273} x& = & 52 \\\Leftrightarrow & x = \frac{52}{273} & & \\\Leftrightarrow & x = \frac{4}{21} & & \\ & V = \left\{ \frac{4}{21} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-5x+\frac{5}{2})& = & 8x+\frac{9}{2} \\\Leftrightarrow & -25x+\frac{25}{2}& = & 8x+\frac{9}{2} \\ & & & \text{kgv van noemers 2 en 2 is 2} \\\Leftrightarrow & \color{blue}{2} .(\frac{-50}{ \color{blue}{2} }x+ \frac{25}{ \color{blue}{2} })& = & (\frac{16}{ \color{blue}{2} }x+ \frac{9}{ \color{blue}{2} }). \color{blue}{2} \\\Leftrightarrow & -50x \color{red}{+25} & = & \color{red}{16x} +9 \\\Leftrightarrow & -50x \color{red}{+25} \color{blue}{-25} \color{blue}{-16x} & = & \color{red}{16x} +9 \color{blue}{-16x} \color{blue}{-25} \\\Leftrightarrow & -50x-16x& = & 9-25 \\\Leftrightarrow & \color{red}{-66} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{-66} & & \\\Leftrightarrow & x = \frac{8}{33} & & \\ & V = \left\{ \frac{8}{33} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{11})& = & 2x+\frac{10}{7} \\\Leftrightarrow & 25x+\frac{25}{11}& = & 2x+\frac{10}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x+ \frac{175}{ \color{blue}{77} })& = & (\frac{154}{ \color{blue}{77} }x+ \frac{110}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{+175} & = & \color{red}{154x} +110 \\\Leftrightarrow & 1925x \color{red}{+175} \color{blue}{-175} \color{blue}{-154x} & = & \color{red}{154x} +110 \color{blue}{-154x} \color{blue}{-175} \\\Leftrightarrow & 1925x-154x& = & 110-175 \\\Leftrightarrow & \color{red}{1771} x& = & -65 \\\Leftrightarrow & x = \frac{-65}{1771} & & \\ & V = \left\{ \frac{-65}{1771} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{3}{11})& = & -9x+\frac{4}{3} \\\Leftrightarrow & -8x+\frac{6}{11}& = & -9x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{18}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+18} & = & \color{red}{-297x} +44 \\\Leftrightarrow & -264x \color{red}{+18} \color{blue}{-18} \color{blue}{+297x} & = & \color{red}{-297x} +44 \color{blue}{+297x} \color{blue}{-18} \\\Leftrightarrow & -264x+297x& = & 44-18 \\\Leftrightarrow & \color{red}{33} x& = & 26 \\\Leftrightarrow & x = \frac{26}{33} & & \\ & V = \left\{ \frac{26}{33} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{4}{5})& = & -7x+\frac{8}{5} \\\Leftrightarrow & -6x+\frac{12}{5}& = & -7x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-30}{ \color{blue}{5} }x+ \frac{12}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -30x \color{red}{+12} & = & \color{red}{-35x} +8 \\\Leftrightarrow & -30x \color{red}{+12} \color{blue}{-12} \color{blue}{+35x} & = & \color{red}{-35x} +8 \color{blue}{+35x} \color{blue}{-12} \\\Leftrightarrow & -30x+35x& = & 8-12 \\\Leftrightarrow & \color{red}{5} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{5} & & \\ & V = \left\{ \frac{-4}{5} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & -8x+\frac{3}{10} \\\Leftrightarrow & -15x-\frac{6}{5}& = & -8x+\frac{3}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-150}{ \color{blue}{10} }x- \frac{12}{ \color{blue}{10} })& = & (\frac{-80}{ \color{blue}{10} }x+ \frac{3}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -150x \color{red}{-12} & = & \color{red}{-80x} +3 \\\Leftrightarrow & -150x \color{red}{-12} \color{blue}{+12} \color{blue}{+80x} & = & \color{red}{-80x} +3 \color{blue}{+80x} \color{blue}{+12} \\\Leftrightarrow & -150x+80x& = & 3+12 \\\Leftrightarrow & \color{red}{-70} x& = & 15 \\\Leftrightarrow & x = \frac{15}{-70} & & \\\Leftrightarrow & x = \frac{-3}{14} & & \\ & V = \left\{ \frac{-3}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (4x-\frac{3}{4})& = & 9x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{15}{4}& = & 9x+\frac{4}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{400}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{180}{ \color{blue}{20} }x+ \frac{16}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 400x \color{red}{-75} & = & \color{red}{180x} +16 \\\Leftrightarrow & 400x \color{red}{-75} \color{blue}{+75} \color{blue}{-180x} & = & \color{red}{180x} +16 \color{blue}{-180x} \color{blue}{+75} \\\Leftrightarrow & 400x-180x& = & 16+75 \\\Leftrightarrow & \color{red}{220} x& = & 91 \\\Leftrightarrow & x = \frac{91}{220} & & \\ & V = \left\{ \frac{91}{220} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-5x-\frac{5}{7})& = & -7x+\frac{2}{3} \\\Leftrightarrow & 30x+\frac{30}{7}& = & -7x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{630}{ \color{blue}{21} }x+ \frac{90}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 630x \color{red}{+90} & = & \color{red}{-147x} +14 \\\Leftrightarrow & 630x \color{red}{+90} \color{blue}{-90} \color{blue}{+147x} & = & \color{red}{-147x} +14 \color{blue}{+147x} \color{blue}{-90} \\\Leftrightarrow & 630x+147x& = & 14-90 \\\Leftrightarrow & \color{red}{777} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{777} & & \\ & V = \left\{ \frac{-76}{777} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{2}{5})& = & -9x+\frac{4}{5} \\\Leftrightarrow & -35x+\frac{14}{5}& = & -9x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-175}{ \color{blue}{5} }x+ \frac{14}{ \color{blue}{5} })& = & (\frac{-45}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -175x \color{red}{+14} & = & \color{red}{-45x} +4 \\\Leftrightarrow & -175x \color{red}{+14} \color{blue}{-14} \color{blue}{+45x} & = & \color{red}{-45x} +4 \color{blue}{+45x} \color{blue}{-14} \\\Leftrightarrow & -175x+45x& = & 4-14 \\\Leftrightarrow & \color{red}{-130} x& = & -10 \\\Leftrightarrow & x = \frac{-10}{-130} & & \\\Leftrightarrow & x = \frac{1}{13} & & \\ & V = \left\{ \frac{1}{13} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{4})& = & -5x+\frac{2}{9} \\\Leftrightarrow & -12x+\frac{15}{4}& = & -5x+\frac{2}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-432}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-180}{ \color{blue}{36} }x+ \frac{8}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -432x \color{red}{+135} & = & \color{red}{-180x} +8 \\\Leftrightarrow & -432x \color{red}{+135} \color{blue}{-135} \color{blue}{+180x} & = & \color{red}{-180x} +8 \color{blue}{+180x} \color{blue}{-135} \\\Leftrightarrow & -432x+180x& = & 8-135 \\\Leftrightarrow & \color{red}{-252} x& = & -127 \\\Leftrightarrow & x = \frac{-127}{-252} & & \\\Leftrightarrow & x = \frac{127}{252} & & \\ & V = \left\{ \frac{127}{252} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{2}{7})& = & -7x+\frac{7}{10} \\\Leftrightarrow & -10x-\frac{10}{7}& = & -7x+\frac{7}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-700}{ \color{blue}{70} }x- \frac{100}{ \color{blue}{70} })& = & (\frac{-490}{ \color{blue}{70} }x+ \frac{49}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -700x \color{red}{-100} & = & \color{red}{-490x} +49 \\\Leftrightarrow & -700x \color{red}{-100} \color{blue}{+100} \color{blue}{+490x} & = & \color{red}{-490x} +49 \color{blue}{+490x} \color{blue}{+100} \\\Leftrightarrow & -700x+490x& = & 49+100 \\\Leftrightarrow & \color{red}{-210} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-210} & & \\\Leftrightarrow & x = \frac{-149}{210} & & \\ & V = \left\{ \frac{-149}{210} \right\} & \\\end{align}\)