Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-3x+\frac{3}{5})& = & 4x+\frac{2}{7} \\\Leftrightarrow & 9x-\frac{9}{5}& = & 4x+\frac{2}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{315}{ \color{blue}{35} }x- \frac{63}{ \color{blue}{35} })& = & (\frac{140}{ \color{blue}{35} }x+ \frac{10}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 315x \color{red}{-63} & = & \color{red}{140x} +10 \\\Leftrightarrow & 315x \color{red}{-63} \color{blue}{+63} \color{blue}{-140x} & = & \color{red}{140x} +10 \color{blue}{-140x} \color{blue}{+63} \\\Leftrightarrow & 315x-140x& = & 10+63 \\\Leftrightarrow & \color{red}{175} x& = & 73 \\\Leftrightarrow & x = \frac{73}{175} & & \\ & V = \left\{ \frac{73}{175} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x+\frac{4}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -20x-\frac{20}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-420}{ \color{blue}{21} }x- \frac{60}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -420x \color{red}{-60} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -420x \color{red}{-60} \color{blue}{+60} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{+60} \\\Leftrightarrow & -420x+147x& = & 28+60 \\\Leftrightarrow & \color{red}{-273} x& = & 88 \\\Leftrightarrow & x = \frac{88}{-273} & & \\\Leftrightarrow & x = \frac{-88}{273} & & \\ & V = \left\{ \frac{-88}{273} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (-2x-\frac{5}{7})& = & -5x+\frac{8}{5} \\\Leftrightarrow & 12x+\frac{30}{7}& = & -5x+\frac{8}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{420}{ \color{blue}{35} }x+ \frac{150}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{56}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 420x \color{red}{+150} & = & \color{red}{-175x} +56 \\\Leftrightarrow & 420x \color{red}{+150} \color{blue}{-150} \color{blue}{+175x} & = & \color{red}{-175x} +56 \color{blue}{+175x} \color{blue}{-150} \\\Leftrightarrow & 420x+175x& = & 56-150 \\\Leftrightarrow & \color{red}{595} x& = & -94 \\\Leftrightarrow & x = \frac{-94}{595} & & \\ & V = \left\{ \frac{-94}{595} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-4x+\frac{4}{7})& = & 9x+\frac{5}{3} \\\Leftrightarrow & 28x-4& = & 9x+\frac{5}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{84}{ \color{blue}{3} }x- \frac{12}{ \color{blue}{3} })& = & (\frac{27}{ \color{blue}{3} }x+ \frac{5}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 84x \color{red}{-12} & = & \color{red}{27x} +5 \\\Leftrightarrow & 84x \color{red}{-12} \color{blue}{+12} \color{blue}{-27x} & = & \color{red}{27x} +5 \color{blue}{-27x} \color{blue}{+12} \\\Leftrightarrow & 84x-27x& = & 5+12 \\\Leftrightarrow & \color{red}{57} x& = & 17 \\\Leftrightarrow & x = \frac{17}{57} & & \\ & V = \left\{ \frac{17}{57} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & 5x+\frac{8}{7} \\\Leftrightarrow & 16x+\frac{20}{3}& = & 5x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{140}{ \color{blue}{21} })& = & (\frac{105}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+140} & = & \color{red}{105x} +24 \\\Leftrightarrow & 336x \color{red}{+140} \color{blue}{-140} \color{blue}{-105x} & = & \color{red}{105x} +24 \color{blue}{-105x} \color{blue}{-140} \\\Leftrightarrow & 336x-105x& = & 24-140 \\\Leftrightarrow & \color{red}{231} x& = & -116 \\\Leftrightarrow & x = \frac{-116}{231} & & \\ & V = \left\{ \frac{-116}{231} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x-\frac{2}{3})& = & -9x+\frac{10}{11} \\\Leftrightarrow & 16x+\frac{8}{3}& = & -9x+\frac{10}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{528}{ \color{blue}{33} }x+ \frac{88}{ \color{blue}{33} })& = & (\frac{-297}{ \color{blue}{33} }x+ \frac{30}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 528x \color{red}{+88} & = & \color{red}{-297x} +30 \\\Leftrightarrow & 528x \color{red}{+88} \color{blue}{-88} \color{blue}{+297x} & = & \color{red}{-297x} +30 \color{blue}{+297x} \color{blue}{-88} \\\Leftrightarrow & 528x+297x& = & 30-88 \\\Leftrightarrow & \color{red}{825} x& = & -58 \\\Leftrightarrow & x = \frac{-58}{825} & & \\ & V = \left\{ \frac{-58}{825} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (3x-\frac{2}{9})& = & 5x+\frac{4}{9} \\\Leftrightarrow & 6x-\frac{4}{9}& = & 5x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{54}{ \color{blue}{9} }x- \frac{4}{ \color{blue}{9} })& = & (\frac{45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 54x \color{red}{-4} & = & \color{red}{45x} +4 \\\Leftrightarrow & 54x \color{red}{-4} \color{blue}{+4} \color{blue}{-45x} & = & \color{red}{45x} +4 \color{blue}{-45x} \color{blue}{+4} \\\Leftrightarrow & 54x-45x& = & 4+4 \\\Leftrightarrow & \color{red}{9} x& = & 8 \\\Leftrightarrow & x = \frac{8}{9} & & \\ & V = \left\{ \frac{8}{9} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x-\frac{5}{7})& = & 9x+\frac{7}{2} \\\Leftrightarrow & -8x-\frac{10}{7}& = & 9x+\frac{7}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-112}{ \color{blue}{14} }x- \frac{20}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{49}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -112x \color{red}{-20} & = & \color{red}{126x} +49 \\\Leftrightarrow & -112x \color{red}{-20} \color{blue}{+20} \color{blue}{-126x} & = & \color{red}{126x} +49 \color{blue}{-126x} \color{blue}{+20} \\\Leftrightarrow & -112x-126x& = & 49+20 \\\Leftrightarrow & \color{red}{-238} x& = & 69 \\\Leftrightarrow & x = \frac{69}{-238} & & \\\Leftrightarrow & x = \frac{-69}{238} & & \\ & V = \left\{ \frac{-69}{238} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{2}{5})& = & -3x+\frac{6}{5} \\\Leftrightarrow & 4x-\frac{4}{5}& = & -3x+\frac{6}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{20}{ \color{blue}{5} }x- \frac{4}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 20x \color{red}{-4} & = & \color{red}{-15x} +6 \\\Leftrightarrow & 20x \color{red}{-4} \color{blue}{+4} \color{blue}{+15x} & = & \color{red}{-15x} +6 \color{blue}{+15x} \color{blue}{+4} \\\Leftrightarrow & 20x+15x& = & 6+4 \\\Leftrightarrow & \color{red}{35} x& = & 10 \\\Leftrightarrow & x = \frac{10}{35} & & \\\Leftrightarrow & x = \frac{2}{7} & & \\ & V = \left\{ \frac{2}{7} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{11})& = & 5x+\frac{2}{7} \\\Leftrightarrow & -9x+\frac{12}{11}& = & 5x+\frac{2}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-693}{ \color{blue}{77} }x+ \frac{84}{ \color{blue}{77} })& = & (\frac{385}{ \color{blue}{77} }x+ \frac{22}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -693x \color{red}{+84} & = & \color{red}{385x} +22 \\\Leftrightarrow & -693x \color{red}{+84} \color{blue}{-84} \color{blue}{-385x} & = & \color{red}{385x} +22 \color{blue}{-385x} \color{blue}{-84} \\\Leftrightarrow & -693x-385x& = & 22-84 \\\Leftrightarrow & \color{red}{-1078} x& = & -62 \\\Leftrightarrow & x = \frac{-62}{-1078} & & \\\Leftrightarrow & x = \frac{31}{539} & & \\ & V = \left\{ \frac{31}{539} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 3x+\frac{7}{3} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 3x+\frac{7}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{120}{ \color{blue}{15} }x- \frac{12}{ \color{blue}{15} })& = & (\frac{45}{ \color{blue}{15} }x+ \frac{35}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 120x \color{red}{-12} & = & \color{red}{45x} +35 \\\Leftrightarrow & 120x \color{red}{-12} \color{blue}{+12} \color{blue}{-45x} & = & \color{red}{45x} +35 \color{blue}{-45x} \color{blue}{+12} \\\Leftrightarrow & 120x-45x& = & 35+12 \\\Leftrightarrow & \color{red}{75} x& = & 47 \\\Leftrightarrow & x = \frac{47}{75} & & \\ & V = \left\{ \frac{47}{75} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-5x-\frac{5}{11})& = & 9x+\frac{4}{9} \\\Leftrightarrow & -20x-\frac{20}{11}& = & 9x+\frac{4}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{-1980}{ \color{blue}{99} }x- \frac{180}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{44}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & -1980x \color{red}{-180} & = & \color{red}{891x} +44 \\\Leftrightarrow & -1980x \color{red}{-180} \color{blue}{+180} \color{blue}{-891x} & = & \color{red}{891x} +44 \color{blue}{-891x} \color{blue}{+180} \\\Leftrightarrow & -1980x-891x& = & 44+180 \\\Leftrightarrow & \color{red}{-2871} x& = & 224 \\\Leftrightarrow & x = \frac{224}{-2871} & & \\\Leftrightarrow & x = \frac{-224}{2871} & & \\ & V = \left\{ \frac{-224}{2871} \right\} & \\\end{align}\)