Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{2}{11})& = & -2x+\frac{2}{3} \\\Leftrightarrow & 9x-\frac{6}{11}& = & -2x+\frac{2}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{297}{ \color{blue}{33} }x- \frac{18}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{22}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 297x \color{red}{-18} & = & \color{red}{-66x} +22 \\\Leftrightarrow & 297x \color{red}{-18} \color{blue}{+18} \color{blue}{+66x} & = & \color{red}{-66x} +22 \color{blue}{+66x} \color{blue}{+18} \\\Leftrightarrow & 297x+66x& = & 22+18 \\\Leftrightarrow & \color{red}{363} x& = & 40 \\\Leftrightarrow & x = \frac{40}{363} & & \\ & V = \left\{ \frac{40}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{4}{5})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x+\frac{12}{5}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-120}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-50x} +25 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +25 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -120x+50x& = & 25-24 \\\Leftrightarrow & \color{red}{-70} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-70} & & \\\Leftrightarrow & x = \frac{-1}{70} & & \\ & V = \left\{ \frac{-1}{70} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x-\frac{4}{3})& = & -2x+\frac{5}{11} \\\Leftrightarrow & 15x+\frac{20}{3}& = & -2x+\frac{5}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{495}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-66}{ \color{blue}{33} }x+ \frac{15}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 495x \color{red}{+220} & = & \color{red}{-66x} +15 \\\Leftrightarrow & 495x \color{red}{+220} \color{blue}{-220} \color{blue}{+66x} & = & \color{red}{-66x} +15 \color{blue}{+66x} \color{blue}{-220} \\\Leftrightarrow & 495x+66x& = & 15-220 \\\Leftrightarrow & \color{red}{561} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{561} & & \\ & V = \left\{ \frac{-205}{561} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{5}{4})& = & -4x+\frac{8}{3} \\\Leftrightarrow & -15x-\frac{15}{4}& = & -4x+\frac{8}{3} \\ & & & \text{kgv van noemers 4 en 3 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-180}{ \color{blue}{12} }x- \frac{45}{ \color{blue}{12} })& = & (\frac{-48}{ \color{blue}{12} }x+ \frac{32}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -180x \color{red}{-45} & = & \color{red}{-48x} +32 \\\Leftrightarrow & -180x \color{red}{-45} \color{blue}{+45} \color{blue}{+48x} & = & \color{red}{-48x} +32 \color{blue}{+48x} \color{blue}{+45} \\\Leftrightarrow & -180x+48x& = & 32+45 \\\Leftrightarrow & \color{red}{-132} x& = & 77 \\\Leftrightarrow & x = \frac{77}{-132} & & \\\Leftrightarrow & x = \frac{-7}{12} & & \\ & V = \left\{ \frac{-7}{12} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x-\frac{2}{5})& = & -7x+\frac{7}{4} \\\Leftrightarrow & -30x+\frac{12}{5}& = & -7x+\frac{7}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-600}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{35}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -600x \color{red}{+48} & = & \color{red}{-140x} +35 \\\Leftrightarrow & -600x \color{red}{+48} \color{blue}{-48} \color{blue}{+140x} & = & \color{red}{-140x} +35 \color{blue}{+140x} \color{blue}{-48} \\\Leftrightarrow & -600x+140x& = & 35-48 \\\Leftrightarrow & \color{red}{-460} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-460} & & \\\Leftrightarrow & x = \frac{13}{460} & & \\ & V = \left\{ \frac{13}{460} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x-\frac{3}{11})& = & 5x+\frac{10}{3} \\\Leftrightarrow & -24x+\frac{18}{11}& = & 5x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-792}{ \color{blue}{33} }x+ \frac{54}{ \color{blue}{33} })& = & (\frac{165}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -792x \color{red}{+54} & = & \color{red}{165x} +110 \\\Leftrightarrow & -792x \color{red}{+54} \color{blue}{-54} \color{blue}{-165x} & = & \color{red}{165x} +110 \color{blue}{-165x} \color{blue}{-54} \\\Leftrightarrow & -792x-165x& = & 110-54 \\\Leftrightarrow & \color{red}{-957} x& = & 56 \\\Leftrightarrow & x = \frac{56}{-957} & & \\\Leftrightarrow & x = \frac{-56}{957} & & \\ & V = \left\{ \frac{-56}{957} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{11})& = & 5x+\frac{7}{4} \\\Leftrightarrow & 8x+\frac{6}{11}& = & 5x+\frac{7}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{352}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{77}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 352x \color{red}{+24} & = & \color{red}{220x} +77 \\\Leftrightarrow & 352x \color{red}{+24} \color{blue}{-24} \color{blue}{-220x} & = & \color{red}{220x} +77 \color{blue}{-220x} \color{blue}{-24} \\\Leftrightarrow & 352x-220x& = & 77-24 \\\Leftrightarrow & \color{red}{132} x& = & 53 \\\Leftrightarrow & x = \frac{53}{132} & & \\ & V = \left\{ \frac{53}{132} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-2x-\frac{2}{9})& = & 3x+\frac{4}{9} \\\Leftrightarrow & 8x+\frac{8}{9}& = & 3x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{72}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} })& = & (\frac{27}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 72x \color{red}{+8} & = & \color{red}{27x} +4 \\\Leftrightarrow & 72x \color{red}{+8} \color{blue}{-8} \color{blue}{-27x} & = & \color{red}{27x} +4 \color{blue}{-27x} \color{blue}{-8} \\\Leftrightarrow & 72x-27x& = & 4-8 \\\Leftrightarrow & \color{red}{45} x& = & -4 \\\Leftrightarrow & x = \frac{-4}{45} & & \\ & V = \left\{ \frac{-4}{45} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-3x-\frac{5}{7})& = & 8x+\frac{4}{5} \\\Leftrightarrow & -18x-\frac{30}{7}& = & 8x+\frac{4}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-630}{ \color{blue}{35} }x- \frac{150}{ \color{blue}{35} })& = & (\frac{280}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -630x \color{red}{-150} & = & \color{red}{280x} +28 \\\Leftrightarrow & -630x \color{red}{-150} \color{blue}{+150} \color{blue}{-280x} & = & \color{red}{280x} +28 \color{blue}{-280x} \color{blue}{+150} \\\Leftrightarrow & -630x-280x& = & 28+150 \\\Leftrightarrow & \color{red}{-910} x& = & 178 \\\Leftrightarrow & x = \frac{178}{-910} & & \\\Leftrightarrow & x = \frac{-89}{455} & & \\ & V = \left\{ \frac{-89}{455} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x-\frac{2}{11})& = & -5x+\frac{9}{2} \\\Leftrightarrow & 21x-\frac{14}{11}& = & -5x+\frac{9}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{462}{ \color{blue}{22} }x- \frac{28}{ \color{blue}{22} })& = & (\frac{-110}{ \color{blue}{22} }x+ \frac{99}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 462x \color{red}{-28} & = & \color{red}{-110x} +99 \\\Leftrightarrow & 462x \color{red}{-28} \color{blue}{+28} \color{blue}{+110x} & = & \color{red}{-110x} +99 \color{blue}{+110x} \color{blue}{+28} \\\Leftrightarrow & 462x+110x& = & 99+28 \\\Leftrightarrow & \color{red}{572} x& = & 127 \\\Leftrightarrow & x = \frac{127}{572} & & \\ & V = \left\{ \frac{127}{572} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{3}{5})& = & -9x+\frac{5}{2} \\\Leftrightarrow & 16x-\frac{12}{5}& = & -9x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 160x \color{red}{-24} & = & \color{red}{-90x} +25 \\\Leftrightarrow & 160x \color{red}{-24} \color{blue}{+24} \color{blue}{+90x} & = & \color{red}{-90x} +25 \color{blue}{+90x} \color{blue}{+24} \\\Leftrightarrow & 160x+90x& = & 25+24 \\\Leftrightarrow & \color{red}{250} x& = & 49 \\\Leftrightarrow & x = \frac{49}{250} & & \\ & V = \left\{ \frac{49}{250} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-5x+\frac{2}{11})& = & 3x+\frac{3}{2} \\\Leftrightarrow & 20x-\frac{8}{11}& = & 3x+\frac{3}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{440}{ \color{blue}{22} }x- \frac{16}{ \color{blue}{22} })& = & (\frac{66}{ \color{blue}{22} }x+ \frac{33}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & 440x \color{red}{-16} & = & \color{red}{66x} +33 \\\Leftrightarrow & 440x \color{red}{-16} \color{blue}{+16} \color{blue}{-66x} & = & \color{red}{66x} +33 \color{blue}{-66x} \color{blue}{+16} \\\Leftrightarrow & 440x-66x& = & 33+16 \\\Leftrightarrow & \color{red}{374} x& = & 49 \\\Leftrightarrow & x = \frac{49}{374} & & \\ & V = \left\{ \frac{49}{374} \right\} & \\\end{align}\)