Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{3}{5})& = & -7x+\frac{3}{4} \\\Leftrightarrow & -16x+\frac{12}{5}& = & -7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-320}{ \color{blue}{20} }x+ \frac{48}{ \color{blue}{20} })& = & (\frac{-140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -320x \color{red}{+48} & = & \color{red}{-140x} +15 \\\Leftrightarrow & -320x \color{red}{+48} \color{blue}{-48} \color{blue}{+140x} & = & \color{red}{-140x} +15 \color{blue}{+140x} \color{blue}{-48} \\\Leftrightarrow & -320x+140x& = & 15-48 \\\Leftrightarrow & \color{red}{-180} x& = & -33 \\\Leftrightarrow & x = \frac{-33}{-180} & & \\\Leftrightarrow & x = \frac{11}{60} & & \\ & V = \left\{ \frac{11}{60} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (4x-\frac{5}{8})& = & 5x+\frac{5}{12} \\\Leftrightarrow & -12x+\frac{15}{8}& = & 5x+\frac{5}{12} \\ & & & \text{kgv van noemers 8 en 12 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-288}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{120}{ \color{blue}{24} }x+ \frac{10}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -288x \color{red}{+45} & = & \color{red}{120x} +10 \\\Leftrightarrow & -288x \color{red}{+45} \color{blue}{-45} \color{blue}{-120x} & = & \color{red}{120x} +10 \color{blue}{-120x} \color{blue}{-45} \\\Leftrightarrow & -288x-120x& = & 10-45 \\\Leftrightarrow & \color{red}{-408} x& = & -35 \\\Leftrightarrow & x = \frac{-35}{-408} & & \\\Leftrightarrow & x = \frac{35}{408} & & \\ & V = \left\{ \frac{35}{408} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (2x+\frac{3}{10})& = & -5x+\frac{7}{10} \\\Leftrightarrow & 6x+\frac{9}{10}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 10 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{60}{ \color{blue}{10} }x+ \frac{9}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & 60x \color{red}{+9} & = & \color{red}{-50x} +7 \\\Leftrightarrow & 60x \color{red}{+9} \color{blue}{-9} \color{blue}{+50x} & = & \color{red}{-50x} +7 \color{blue}{+50x} \color{blue}{-9} \\\Leftrightarrow & 60x+50x& = & 7-9 \\\Leftrightarrow & \color{red}{110} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{110} & & \\\Leftrightarrow & x = \frac{-1}{55} & & \\ & V = \left\{ \frac{-1}{55} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{4}{11})& = & 4x+\frac{3}{10} \\\Leftrightarrow & -15x+\frac{12}{11}& = & 4x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1650}{ \color{blue}{110} }x+ \frac{120}{ \color{blue}{110} })& = & (\frac{440}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1650x \color{red}{+120} & = & \color{red}{440x} +33 \\\Leftrightarrow & -1650x \color{red}{+120} \color{blue}{-120} \color{blue}{-440x} & = & \color{red}{440x} +33 \color{blue}{-440x} \color{blue}{-120} \\\Leftrightarrow & -1650x-440x& = & 33-120 \\\Leftrightarrow & \color{red}{-2090} x& = & -87 \\\Leftrightarrow & x = \frac{-87}{-2090} & & \\\Leftrightarrow & x = \frac{87}{2090} & & \\ & V = \left\{ \frac{87}{2090} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{3}{11})& = & 5x+\frac{5}{4} \\\Leftrightarrow & -12x+\frac{18}{11}& = & 5x+\frac{5}{4} \\ & & & \text{kgv van noemers 11 en 4 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-528}{ \color{blue}{44} }x+ \frac{72}{ \color{blue}{44} })& = & (\frac{220}{ \color{blue}{44} }x+ \frac{55}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -528x \color{red}{+72} & = & \color{red}{220x} +55 \\\Leftrightarrow & -528x \color{red}{+72} \color{blue}{-72} \color{blue}{-220x} & = & \color{red}{220x} +55 \color{blue}{-220x} \color{blue}{-72} \\\Leftrightarrow & -528x-220x& = & 55-72 \\\Leftrightarrow & \color{red}{-748} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-748} & & \\\Leftrightarrow & x = \frac{1}{44} & & \\ & V = \left\{ \frac{1}{44} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{4}{7})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 20x-\frac{20}{7}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{700}{ \color{blue}{35} }x- \frac{100}{ \color{blue}{35} })& = & (\frac{-105}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 700x \color{red}{-100} & = & \color{red}{-105x} +42 \\\Leftrightarrow & 700x \color{red}{-100} \color{blue}{+100} \color{blue}{+105x} & = & \color{red}{-105x} +42 \color{blue}{+105x} \color{blue}{+100} \\\Leftrightarrow & 700x+105x& = & 42+100 \\\Leftrightarrow & \color{red}{805} x& = & 142 \\\Leftrightarrow & x = \frac{142}{805} & & \\ & V = \left\{ \frac{142}{805} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{9})& = & 9x+\frac{7}{8} \\\Leftrightarrow & 4x+\frac{4}{9}& = & 9x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{288}{ \color{blue}{72} }x+ \frac{32}{ \color{blue}{72} })& = & (\frac{648}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & 288x \color{red}{+32} & = & \color{red}{648x} +63 \\\Leftrightarrow & 288x \color{red}{+32} \color{blue}{-32} \color{blue}{-648x} & = & \color{red}{648x} +63 \color{blue}{-648x} \color{blue}{-32} \\\Leftrightarrow & 288x-648x& = & 63-32 \\\Leftrightarrow & \color{red}{-360} x& = & 31 \\\Leftrightarrow & x = \frac{31}{-360} & & \\\Leftrightarrow & x = \frac{-31}{360} & & \\ & V = \left\{ \frac{-31}{360} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{9})& = & 7x+\frac{5}{9} \\\Leftrightarrow & -20x+\frac{20}{9}& = & 7x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-180}{ \color{blue}{9} }x+ \frac{20}{ \color{blue}{9} })& = & (\frac{63}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -180x \color{red}{+20} & = & \color{red}{63x} +5 \\\Leftrightarrow & -180x \color{red}{+20} \color{blue}{-20} \color{blue}{-63x} & = & \color{red}{63x} +5 \color{blue}{-63x} \color{blue}{-20} \\\Leftrightarrow & -180x-63x& = & 5-20 \\\Leftrightarrow & \color{red}{-243} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-243} & & \\\Leftrightarrow & x = \frac{5}{81} & & \\ & V = \left\{ \frac{5}{81} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (4x-\frac{5}{12})& = & -9x+\frac{4}{7} \\\Leftrightarrow & 28x-\frac{35}{12}& = & -9x+\frac{4}{7} \\ & & & \text{kgv van noemers 12 en 7 is 84} \\\Leftrightarrow & \color{blue}{84} .(\frac{2352}{ \color{blue}{84} }x- \frac{245}{ \color{blue}{84} })& = & (\frac{-756}{ \color{blue}{84} }x+ \frac{48}{ \color{blue}{84} }). \color{blue}{84} \\\Leftrightarrow & 2352x \color{red}{-245} & = & \color{red}{-756x} +48 \\\Leftrightarrow & 2352x \color{red}{-245} \color{blue}{+245} \color{blue}{+756x} & = & \color{red}{-756x} +48 \color{blue}{+756x} \color{blue}{+245} \\\Leftrightarrow & 2352x+756x& = & 48+245 \\\Leftrightarrow & \color{red}{3108} x& = & 293 \\\Leftrightarrow & x = \frac{293}{3108} & & \\ & V = \left\{ \frac{293}{3108} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{3}{4})& = & -8x+\frac{10}{7} \\\Leftrightarrow & -15x+\frac{9}{4}& = & -8x+\frac{10}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-420}{ \color{blue}{28} }x+ \frac{63}{ \color{blue}{28} })& = & (\frac{-224}{ \color{blue}{28} }x+ \frac{40}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -420x \color{red}{+63} & = & \color{red}{-224x} +40 \\\Leftrightarrow & -420x \color{red}{+63} \color{blue}{-63} \color{blue}{+224x} & = & \color{red}{-224x} +40 \color{blue}{+224x} \color{blue}{-63} \\\Leftrightarrow & -420x+224x& = & 40-63 \\\Leftrightarrow & \color{red}{-196} x& = & -23 \\\Leftrightarrow & x = \frac{-23}{-196} & & \\\Leftrightarrow & x = \frac{23}{196} & & \\ & V = \left\{ \frac{23}{196} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{2}{7})& = & -7x+\frac{9}{7} \\\Leftrightarrow & 12x-\frac{8}{7}& = & -7x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{84}{ \color{blue}{7} }x- \frac{8}{ \color{blue}{7} })& = & (\frac{-49}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 84x \color{red}{-8} & = & \color{red}{-49x} +9 \\\Leftrightarrow & 84x \color{red}{-8} \color{blue}{+8} \color{blue}{+49x} & = & \color{red}{-49x} +9 \color{blue}{+49x} \color{blue}{+8} \\\Leftrightarrow & 84x+49x& = & 9+8 \\\Leftrightarrow & \color{red}{133} x& = & 17 \\\Leftrightarrow & x = \frac{17}{133} & & \\ & V = \left\{ \frac{17}{133} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (3x+\frac{4}{9})& = & 2x+\frac{2}{11} \\\Leftrightarrow & 21x+\frac{28}{9}& = & 2x+\frac{2}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{2079}{ \color{blue}{99} }x+ \frac{308}{ \color{blue}{99} })& = & (\frac{198}{ \color{blue}{99} }x+ \frac{18}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 2079x \color{red}{+308} & = & \color{red}{198x} +18 \\\Leftrightarrow & 2079x \color{red}{+308} \color{blue}{-308} \color{blue}{-198x} & = & \color{red}{198x} +18 \color{blue}{-198x} \color{blue}{-308} \\\Leftrightarrow & 2079x-198x& = & 18-308 \\\Leftrightarrow & \color{red}{1881} x& = & -290 \\\Leftrightarrow & x = \frac{-290}{1881} & & \\ & V = \left\{ \frac{-290}{1881} \right\} & \\\end{align}\)