Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{4}{11})& = & -3x+\frac{4}{3} \\\Leftrightarrow & -14x-\frac{28}{11}& = & -3x+\frac{4}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-462}{ \color{blue}{33} }x- \frac{84}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{44}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -462x \color{red}{-84} & = & \color{red}{-99x} +44 \\\Leftrightarrow & -462x \color{red}{-84} \color{blue}{+84} \color{blue}{+99x} & = & \color{red}{-99x} +44 \color{blue}{+99x} \color{blue}{+84} \\\Leftrightarrow & -462x+99x& = & 44+84 \\\Leftrightarrow & \color{red}{-363} x& = & 128 \\\Leftrightarrow & x = \frac{128}{-363} & & \\\Leftrightarrow & x = \frac{-128}{363} & & \\ & V = \left\{ \frac{-128}{363} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{7})& = & 3x+\frac{4}{3} \\\Leftrightarrow & 16x+\frac{20}{7}& = & 3x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{336}{ \color{blue}{21} }x+ \frac{60}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 336x \color{red}{+60} & = & \color{red}{63x} +28 \\\Leftrightarrow & 336x \color{red}{+60} \color{blue}{-60} \color{blue}{-63x} & = & \color{red}{63x} +28 \color{blue}{-63x} \color{blue}{-60} \\\Leftrightarrow & 336x-63x& = & 28-60 \\\Leftrightarrow & \color{red}{273} x& = & -32 \\\Leftrightarrow & x = \frac{-32}{273} & & \\ & V = \left\{ \frac{-32}{273} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x+\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & -12x+\frac{12}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{132}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+132} & = & \color{red}{275x} +25 \\\Leftrightarrow & -660x \color{red}{+132} \color{blue}{-132} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{-132} \\\Leftrightarrow & -660x-275x& = & 25-132 \\\Leftrightarrow & \color{red}{-935} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-935} & & \\\Leftrightarrow & x = \frac{107}{935} & & \\ & V = \left\{ \frac{107}{935} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x+\frac{2}{5})& = & 5x+\frac{5}{11} \\\Leftrightarrow & 8x-\frac{4}{5}& = & 5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{44}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-44} & = & \color{red}{275x} +25 \\\Leftrightarrow & 440x \color{red}{-44} \color{blue}{+44} \color{blue}{-275x} & = & \color{red}{275x} +25 \color{blue}{-275x} \color{blue}{+44} \\\Leftrightarrow & 440x-275x& = & 25+44 \\\Leftrightarrow & \color{red}{165} x& = & 69 \\\Leftrightarrow & x = \frac{69}{165} & & \\\Leftrightarrow & x = \frac{23}{55} & & \\ & V = \left\{ \frac{23}{55} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{2}{5})& = & 4x+\frac{4}{5} \\\Leftrightarrow & 9x+\frac{6}{5}& = & 4x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{45}{ \color{blue}{5} }x+ \frac{6}{ \color{blue}{5} })& = & (\frac{20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 45x \color{red}{+6} & = & \color{red}{20x} +4 \\\Leftrightarrow & 45x \color{red}{+6} \color{blue}{-6} \color{blue}{-20x} & = & \color{red}{20x} +4 \color{blue}{-20x} \color{blue}{-6} \\\Leftrightarrow & 45x-20x& = & 4-6 \\\Leftrightarrow & \color{red}{25} x& = & -2 \\\Leftrightarrow & x = \frac{-2}{25} & & \\ & V = \left\{ \frac{-2}{25} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x+\frac{5}{7})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -15x+\frac{15}{7}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-945}{ \color{blue}{63} }x+ \frac{135}{ \color{blue}{63} })& = & (\frac{504}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -945x \color{red}{+135} & = & \color{red}{504x} +28 \\\Leftrightarrow & -945x \color{red}{+135} \color{blue}{-135} \color{blue}{-504x} & = & \color{red}{504x} +28 \color{blue}{-504x} \color{blue}{-135} \\\Leftrightarrow & -945x-504x& = & 28-135 \\\Leftrightarrow & \color{red}{-1449} x& = & -107 \\\Leftrightarrow & x = \frac{-107}{-1449} & & \\\Leftrightarrow & x = \frac{107}{1449} & & \\ & V = \left\{ \frac{107}{1449} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & -7x+\frac{8}{11} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{8}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-264}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{32}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -264x \color{red}{+165} & = & \color{red}{-308x} +32 \\\Leftrightarrow & -264x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +32 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & -264x+308x& = & 32-165 \\\Leftrightarrow & \color{red}{44} x& = & -133 \\\Leftrightarrow & x = \frac{-133}{44} & & \\ & V = \left\{ \frac{-133}{44} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x-\frac{3}{5})& = & -5x+\frac{8}{3} \\\Leftrightarrow & -24x-\frac{18}{5}& = & -5x+\frac{8}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{-360}{ \color{blue}{15} }x- \frac{54}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{40}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & -360x \color{red}{-54} & = & \color{red}{-75x} +40 \\\Leftrightarrow & -360x \color{red}{-54} \color{blue}{+54} \color{blue}{+75x} & = & \color{red}{-75x} +40 \color{blue}{+75x} \color{blue}{+54} \\\Leftrightarrow & -360x+75x& = & 40+54 \\\Leftrightarrow & \color{red}{-285} x& = & 94 \\\Leftrightarrow & x = \frac{94}{-285} & & \\\Leftrightarrow & x = \frac{-94}{285} & & \\ & V = \left\{ \frac{-94}{285} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{5})& = & -7x+\frac{9}{5} \\\Leftrightarrow & -16x+\frac{8}{5}& = & -7x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-80}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} })& = & (\frac{-35}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -80x \color{red}{+8} & = & \color{red}{-35x} +9 \\\Leftrightarrow & -80x \color{red}{+8} \color{blue}{-8} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{-8} \\\Leftrightarrow & -80x+35x& = & 9-8 \\\Leftrightarrow & \color{red}{-45} x& = & 1 \\\Leftrightarrow & x = \frac{1}{-45} & & \\\Leftrightarrow & x = \frac{-1}{45} & & \\ & V = \left\{ \frac{-1}{45} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-5x-\frac{2}{5})& = & -8x+\frac{8}{5} \\\Leftrightarrow & -15x-\frac{6}{5}& = & -8x+\frac{8}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-75}{ \color{blue}{5} }x- \frac{6}{ \color{blue}{5} })& = & (\frac{-40}{ \color{blue}{5} }x+ \frac{8}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -75x \color{red}{-6} & = & \color{red}{-40x} +8 \\\Leftrightarrow & -75x \color{red}{-6} \color{blue}{+6} \color{blue}{+40x} & = & \color{red}{-40x} +8 \color{blue}{+40x} \color{blue}{+6} \\\Leftrightarrow & -75x+40x& = & 8+6 \\\Leftrightarrow & \color{red}{-35} x& = & 14 \\\Leftrightarrow & x = \frac{14}{-35} & & \\\Leftrightarrow & x = \frac{-2}{5} & & \\ & V = \left\{ \frac{-2}{5} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (2x-\frac{5}{4})& = & -7x+\frac{8}{9} \\\Leftrightarrow & -6x+\frac{15}{4}& = & -7x+\frac{8}{9} \\ & & & \text{kgv van noemers 4 en 9 is 36} \\\Leftrightarrow & \color{blue}{36} .(\frac{-216}{ \color{blue}{36} }x+ \frac{135}{ \color{blue}{36} })& = & (\frac{-252}{ \color{blue}{36} }x+ \frac{32}{ \color{blue}{36} }). \color{blue}{36} \\\Leftrightarrow & -216x \color{red}{+135} & = & \color{red}{-252x} +32 \\\Leftrightarrow & -216x \color{red}{+135} \color{blue}{-135} \color{blue}{+252x} & = & \color{red}{-252x} +32 \color{blue}{+252x} \color{blue}{-135} \\\Leftrightarrow & -216x+252x& = & 32-135 \\\Leftrightarrow & \color{red}{36} x& = & -103 \\\Leftrightarrow & x = \frac{-103}{36} & & \\ & V = \left\{ \frac{-103}{36} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (2x+\frac{3}{7})& = & -5x+\frac{3}{11} \\\Leftrightarrow & -4x-\frac{6}{7}& = & -5x+\frac{3}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-308}{ \color{blue}{77} }x- \frac{66}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{21}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -308x \color{red}{-66} & = & \color{red}{-385x} +21 \\\Leftrightarrow & -308x \color{red}{-66} \color{blue}{+66} \color{blue}{+385x} & = & \color{red}{-385x} +21 \color{blue}{+385x} \color{blue}{+66} \\\Leftrightarrow & -308x+385x& = & 21+66 \\\Leftrightarrow & \color{red}{77} x& = & 87 \\\Leftrightarrow & x = \frac{87}{77} & & \\ & V = \left\{ \frac{87}{77} \right\} & \\\end{align}\)