Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{4}{9})& = & -7x+\frac{10}{9} \\\Leftrightarrow & -16x+\frac{16}{9}& = & -7x+\frac{10}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-144}{ \color{blue}{9} }x+ \frac{16}{ \color{blue}{9} })& = & (\frac{-63}{ \color{blue}{9} }x+ \frac{10}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -144x \color{red}{+16} & = & \color{red}{-63x} +10 \\\Leftrightarrow & -144x \color{red}{+16} \color{blue}{-16} \color{blue}{+63x} & = & \color{red}{-63x} +10 \color{blue}{+63x} \color{blue}{-16} \\\Leftrightarrow & -144x+63x& = & 10-16 \\\Leftrightarrow & \color{red}{-81} x& = & -6 \\\Leftrightarrow & x = \frac{-6}{-81} & & \\\Leftrightarrow & x = \frac{2}{27} & & \\ & V = \left\{ \frac{2}{27} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{7})& = & -5x+\frac{3}{8} \\\Leftrightarrow & -12x+\frac{6}{7}& = & -5x+\frac{3}{8} \\ & & & \text{kgv van noemers 7 en 8 is 56} \\\Leftrightarrow & \color{blue}{56} .(\frac{-672}{ \color{blue}{56} }x+ \frac{48}{ \color{blue}{56} })& = & (\frac{-280}{ \color{blue}{56} }x+ \frac{21}{ \color{blue}{56} }). \color{blue}{56} \\\Leftrightarrow & -672x \color{red}{+48} & = & \color{red}{-280x} +21 \\\Leftrightarrow & -672x \color{red}{+48} \color{blue}{-48} \color{blue}{+280x} & = & \color{red}{-280x} +21 \color{blue}{+280x} \color{blue}{-48} \\\Leftrightarrow & -672x+280x& = & 21-48 \\\Leftrightarrow & \color{red}{-392} x& = & -27 \\\Leftrightarrow & x = \frac{-27}{-392} & & \\\Leftrightarrow & x = \frac{27}{392} & & \\ & V = \left\{ \frac{27}{392} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{2}{11})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -20x-\frac{10}{11}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-440}{ \color{blue}{22} }x- \frac{20}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{55}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -440x \color{red}{-20} & = & \color{red}{154x} +55 \\\Leftrightarrow & -440x \color{red}{-20} \color{blue}{+20} \color{blue}{-154x} & = & \color{red}{154x} +55 \color{blue}{-154x} \color{blue}{+20} \\\Leftrightarrow & -440x-154x& = & 55+20 \\\Leftrightarrow & \color{red}{-594} x& = & 75 \\\Leftrightarrow & x = \frac{75}{-594} & & \\\Leftrightarrow & x = \frac{-25}{198} & & \\ & V = \left\{ \frac{-25}{198} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x+\frac{5}{3})& = & 3x+\frac{6}{7} \\\Leftrightarrow & -8x-\frac{20}{3}& = & 3x+\frac{6}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{140}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{18}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-140} & = & \color{red}{63x} +18 \\\Leftrightarrow & -168x \color{red}{-140} \color{blue}{+140} \color{blue}{-63x} & = & \color{red}{63x} +18 \color{blue}{-63x} \color{blue}{+140} \\\Leftrightarrow & -168x-63x& = & 18+140 \\\Leftrightarrow & \color{red}{-231} x& = & 158 \\\Leftrightarrow & x = \frac{158}{-231} & & \\\Leftrightarrow & x = \frac{-158}{231} & & \\ & V = \left\{ \frac{-158}{231} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{2}{9})& = & -5x+\frac{2}{7} \\\Leftrightarrow & -4x-\frac{4}{9}& = & -5x+\frac{2}{7} \\ & & & \text{kgv van noemers 9 en 7 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-252}{ \color{blue}{63} }x- \frac{28}{ \color{blue}{63} })& = & (\frac{-315}{ \color{blue}{63} }x+ \frac{18}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -252x \color{red}{-28} & = & \color{red}{-315x} +18 \\\Leftrightarrow & -252x \color{red}{-28} \color{blue}{+28} \color{blue}{+315x} & = & \color{red}{-315x} +18 \color{blue}{+315x} \color{blue}{+28} \\\Leftrightarrow & -252x+315x& = & 18+28 \\\Leftrightarrow & \color{red}{63} x& = & 46 \\\Leftrightarrow & x = \frac{46}{63} & & \\ & V = \left\{ \frac{46}{63} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{5})& = & 9x+\frac{10}{7} \\\Leftrightarrow & 8x+\frac{6}{5}& = & 9x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x+ \frac{42}{ \color{blue}{35} })& = & (\frac{315}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{+42} & = & \color{red}{315x} +50 \\\Leftrightarrow & 280x \color{red}{+42} \color{blue}{-42} \color{blue}{-315x} & = & \color{red}{315x} +50 \color{blue}{-315x} \color{blue}{-42} \\\Leftrightarrow & 280x-315x& = & 50-42 \\\Leftrightarrow & \color{red}{-35} x& = & 8 \\\Leftrightarrow & x = \frac{8}{-35} & & \\\Leftrightarrow & x = \frac{-8}{35} & & \\ & V = \left\{ \frac{-8}{35} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-5x-\frac{2}{5})& = & 3x+\frac{10}{7} \\\Leftrightarrow & 10x+\frac{4}{5}& = & 3x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{350}{ \color{blue}{35} }x+ \frac{28}{ \color{blue}{35} })& = & (\frac{105}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 350x \color{red}{+28} & = & \color{red}{105x} +50 \\\Leftrightarrow & 350x \color{red}{+28} \color{blue}{-28} \color{blue}{-105x} & = & \color{red}{105x} +50 \color{blue}{-105x} \color{blue}{-28} \\\Leftrightarrow & 350x-105x& = & 50-28 \\\Leftrightarrow & \color{red}{245} x& = & 22 \\\Leftrightarrow & x = \frac{22}{245} & & \\ & V = \left\{ \frac{22}{245} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x+\frac{3}{5})& = & 7x+\frac{5}{2} \\\Leftrightarrow & -16x-\frac{12}{5}& = & 7x+\frac{5}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-160}{ \color{blue}{10} }x- \frac{24}{ \color{blue}{10} })& = & (\frac{70}{ \color{blue}{10} }x+ \frac{25}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -160x \color{red}{-24} & = & \color{red}{70x} +25 \\\Leftrightarrow & -160x \color{red}{-24} \color{blue}{+24} \color{blue}{-70x} & = & \color{red}{70x} +25 \color{blue}{-70x} \color{blue}{+24} \\\Leftrightarrow & -160x-70x& = & 25+24 \\\Leftrightarrow & \color{red}{-230} x& = & 49 \\\Leftrightarrow & x = \frac{49}{-230} & & \\\Leftrightarrow & x = \frac{-49}{230} & & \\ & V = \left\{ \frac{-49}{230} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{3}{8})& = & 3x+\frac{3}{4} \\\Leftrightarrow & 14x+\frac{21}{8}& = & 3x+\frac{3}{4} \\ & & & \text{kgv van noemers 8 en 4 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{112}{ \color{blue}{8} }x+ \frac{21}{ \color{blue}{8} })& = & (\frac{24}{ \color{blue}{8} }x+ \frac{6}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & 112x \color{red}{+21} & = & \color{red}{24x} +6 \\\Leftrightarrow & 112x \color{red}{+21} \color{blue}{-21} \color{blue}{-24x} & = & \color{red}{24x} +6 \color{blue}{-24x} \color{blue}{-21} \\\Leftrightarrow & 112x-24x& = & 6-21 \\\Leftrightarrow & \color{red}{88} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{88} & & \\ & V = \left\{ \frac{-15}{88} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (5x+\frac{3}{4})& = & -8x+\frac{7}{5} \\\Leftrightarrow & -25x-\frac{15}{4}& = & -8x+\frac{7}{5} \\ & & & \text{kgv van noemers 4 en 5 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{-160}{ \color{blue}{20} }x+ \frac{28}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -500x \color{red}{-75} & = & \color{red}{-160x} +28 \\\Leftrightarrow & -500x \color{red}{-75} \color{blue}{+75} \color{blue}{+160x} & = & \color{red}{-160x} +28 \color{blue}{+160x} \color{blue}{+75} \\\Leftrightarrow & -500x+160x& = & 28+75 \\\Leftrightarrow & \color{red}{-340} x& = & 103 \\\Leftrightarrow & x = \frac{103}{-340} & & \\\Leftrightarrow & x = \frac{-103}{340} & & \\ & V = \left\{ \frac{-103}{340} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-4x-\frac{5}{8})& = & -5x+\frac{7}{3} \\\Leftrightarrow & 12x+\frac{15}{8}& = & -5x+\frac{7}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{288}{ \color{blue}{24} }x+ \frac{45}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{56}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & 288x \color{red}{+45} & = & \color{red}{-120x} +56 \\\Leftrightarrow & 288x \color{red}{+45} \color{blue}{-45} \color{blue}{+120x} & = & \color{red}{-120x} +56 \color{blue}{+120x} \color{blue}{-45} \\\Leftrightarrow & 288x+120x& = & 56-45 \\\Leftrightarrow & \color{red}{408} x& = & 11 \\\Leftrightarrow & x = \frac{11}{408} & & \\ & V = \left\{ \frac{11}{408} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{3}{11})& = & 4x+\frac{4}{5} \\\Leftrightarrow & -28x-\frac{21}{11}& = & 4x+\frac{4}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x- \frac{105}{ \color{blue}{55} })& = & (\frac{220}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{-105} & = & \color{red}{220x} +44 \\\Leftrightarrow & -1540x \color{red}{-105} \color{blue}{+105} \color{blue}{-220x} & = & \color{red}{220x} +44 \color{blue}{-220x} \color{blue}{+105} \\\Leftrightarrow & -1540x-220x& = & 44+105 \\\Leftrightarrow & \color{red}{-1760} x& = & 149 \\\Leftrightarrow & x = \frac{149}{-1760} & & \\\Leftrightarrow & x = \frac{-149}{1760} & & \\ & V = \left\{ \frac{-149}{1760} \right\} & \\\end{align}\)