Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x+\frac{3}{8})& = & -7x+\frac{9}{2} \\\Leftrightarrow & -28x-\frac{21}{8}& = & -7x+\frac{9}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-224}{ \color{blue}{8} }x- \frac{21}{ \color{blue}{8} })& = & (\frac{-56}{ \color{blue}{8} }x+ \frac{36}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -224x \color{red}{-21} & = & \color{red}{-56x} +36 \\\Leftrightarrow & -224x \color{red}{-21} \color{blue}{+21} \color{blue}{+56x} & = & \color{red}{-56x} +36 \color{blue}{+56x} \color{blue}{+21} \\\Leftrightarrow & -224x+56x& = & 36+21 \\\Leftrightarrow & \color{red}{-168} x& = & 57 \\\Leftrightarrow & x = \frac{57}{-168} & & \\\Leftrightarrow & x = \frac{-19}{56} & & \\ & V = \left\{ \frac{-19}{56} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{3}{11})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -24x-\frac{18}{11}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1320}{ \color{blue}{55} }x- \frac{90}{ \color{blue}{55} })& = & (\frac{-385}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1320x \color{red}{-90} & = & \color{red}{-385x} +66 \\\Leftrightarrow & -1320x \color{red}{-90} \color{blue}{+90} \color{blue}{+385x} & = & \color{red}{-385x} +66 \color{blue}{+385x} \color{blue}{+90} \\\Leftrightarrow & -1320x+385x& = & 66+90 \\\Leftrightarrow & \color{red}{-935} x& = & 156 \\\Leftrightarrow & x = \frac{156}{-935} & & \\\Leftrightarrow & x = \frac{-156}{935} & & \\ & V = \left\{ \frac{-156}{935} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{5}{4})& = & -9x+\frac{5}{6} \\\Leftrightarrow & 14x-\frac{35}{4}& = & -9x+\frac{5}{6} \\ & & & \text{kgv van noemers 4 en 6 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{168}{ \color{blue}{12} }x- \frac{105}{ \color{blue}{12} })& = & (\frac{-108}{ \color{blue}{12} }x+ \frac{10}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 168x \color{red}{-105} & = & \color{red}{-108x} +10 \\\Leftrightarrow & 168x \color{red}{-105} \color{blue}{+105} \color{blue}{+108x} & = & \color{red}{-108x} +10 \color{blue}{+108x} \color{blue}{+105} \\\Leftrightarrow & 168x+108x& = & 10+105 \\\Leftrightarrow & \color{red}{276} x& = & 115 \\\Leftrightarrow & x = \frac{115}{276} & & \\\Leftrightarrow & x = \frac{5}{12} & & \\ & V = \left\{ \frac{5}{12} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-3x-\frac{4}{9})& = & 5x+\frac{8}{11} \\\Leftrightarrow & 6x+\frac{8}{9}& = & 5x+\frac{8}{11} \\ & & & \text{kgv van noemers 9 en 11 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{594}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} })& = & (\frac{495}{ \color{blue}{99} }x+ \frac{72}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 594x \color{red}{+88} & = & \color{red}{495x} +72 \\\Leftrightarrow & 594x \color{red}{+88} \color{blue}{-88} \color{blue}{-495x} & = & \color{red}{495x} +72 \color{blue}{-495x} \color{blue}{-88} \\\Leftrightarrow & 594x-495x& = & 72-88 \\\Leftrightarrow & \color{red}{99} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{99} & & \\ & V = \left\{ \frac{-16}{99} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (2x-\frac{4}{11})& = & 5x+\frac{7}{2} \\\Leftrightarrow & -12x+\frac{24}{11}& = & 5x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-264}{ \color{blue}{22} }x+ \frac{48}{ \color{blue}{22} })& = & (\frac{110}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -264x \color{red}{+48} & = & \color{red}{110x} +77 \\\Leftrightarrow & -264x \color{red}{+48} \color{blue}{-48} \color{blue}{-110x} & = & \color{red}{110x} +77 \color{blue}{-110x} \color{blue}{-48} \\\Leftrightarrow & -264x-110x& = & 77-48 \\\Leftrightarrow & \color{red}{-374} x& = & 29 \\\Leftrightarrow & x = \frac{29}{-374} & & \\\Leftrightarrow & x = \frac{-29}{374} & & \\ & V = \left\{ \frac{-29}{374} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-4x+\frac{2}{5})& = & -7x+\frac{7}{6} \\\Leftrightarrow & -16x+\frac{8}{5}& = & -7x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{-480}{ \color{blue}{30} }x+ \frac{48}{ \color{blue}{30} })& = & (\frac{-210}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & -480x \color{red}{+48} & = & \color{red}{-210x} +35 \\\Leftrightarrow & -480x \color{red}{+48} \color{blue}{-48} \color{blue}{+210x} & = & \color{red}{-210x} +35 \color{blue}{+210x} \color{blue}{-48} \\\Leftrightarrow & -480x+210x& = & 35-48 \\\Leftrightarrow & \color{red}{-270} x& = & -13 \\\Leftrightarrow & x = \frac{-13}{-270} & & \\\Leftrightarrow & x = \frac{13}{270} & & \\ & V = \left\{ \frac{13}{270} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x-\frac{5}{8})& = & -9x+\frac{7}{2} \\\Leftrightarrow & -35x-\frac{35}{8}& = & -9x+\frac{7}{2} \\ & & & \text{kgv van noemers 8 en 2 is 8} \\\Leftrightarrow & \color{blue}{8} .(\frac{-280}{ \color{blue}{8} }x- \frac{35}{ \color{blue}{8} })& = & (\frac{-72}{ \color{blue}{8} }x+ \frac{28}{ \color{blue}{8} }). \color{blue}{8} \\\Leftrightarrow & -280x \color{red}{-35} & = & \color{red}{-72x} +28 \\\Leftrightarrow & -280x \color{red}{-35} \color{blue}{+35} \color{blue}{+72x} & = & \color{red}{-72x} +28 \color{blue}{+72x} \color{blue}{+35} \\\Leftrightarrow & -280x+72x& = & 28+35 \\\Leftrightarrow & \color{red}{-208} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-208} & & \\\Leftrightarrow & x = \frac{-63}{208} & & \\ & V = \left\{ \frac{-63}{208} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -5x+\frac{9}{7} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -5x+\frac{9}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{28}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-35}{ \color{blue}{7} }x+ \frac{9}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 28x \color{red}{+6} & = & \color{red}{-35x} +9 \\\Leftrightarrow & 28x \color{red}{+6} \color{blue}{-6} \color{blue}{+35x} & = & \color{red}{-35x} +9 \color{blue}{+35x} \color{blue}{-6} \\\Leftrightarrow & 28x+35x& = & 9-6 \\\Leftrightarrow & \color{red}{63} x& = & 3 \\\Leftrightarrow & x = \frac{3}{63} & & \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{2}{11})& = & 4x+\frac{7}{12} \\\Leftrightarrow & -15x+\frac{10}{11}& = & 4x+\frac{7}{12} \\ & & & \text{kgv van noemers 11 en 12 is 132} \\\Leftrightarrow & \color{blue}{132} .(\frac{-1980}{ \color{blue}{132} }x+ \frac{120}{ \color{blue}{132} })& = & (\frac{528}{ \color{blue}{132} }x+ \frac{77}{ \color{blue}{132} }). \color{blue}{132} \\\Leftrightarrow & -1980x \color{red}{+120} & = & \color{red}{528x} +77 \\\Leftrightarrow & -1980x \color{red}{+120} \color{blue}{-120} \color{blue}{-528x} & = & \color{red}{528x} +77 \color{blue}{-528x} \color{blue}{-120} \\\Leftrightarrow & -1980x-528x& = & 77-120 \\\Leftrightarrow & \color{red}{-2508} x& = & -43 \\\Leftrightarrow & x = \frac{-43}{-2508} & & \\\Leftrightarrow & x = \frac{43}{2508} & & \\ & V = \left\{ \frac{43}{2508} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{3}{7})& = & -9x+\frac{6}{11} \\\Leftrightarrow & 4x+\frac{6}{7}& = & -9x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{+66} & = & \color{red}{-693x} +42 \\\Leftrightarrow & 308x \color{red}{+66} \color{blue}{-66} \color{blue}{+693x} & = & \color{red}{-693x} +42 \color{blue}{+693x} \color{blue}{-66} \\\Leftrightarrow & 308x+693x& = & 42-66 \\\Leftrightarrow & \color{red}{1001} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{1001} & & \\ & V = \left\{ \frac{-24}{1001} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{4}{5})& = & -5x+\frac{4}{3} \\\Leftrightarrow & 12x+\frac{12}{5}& = & -5x+\frac{4}{3} \\ & & & \text{kgv van noemers 5 en 3 is 15} \\\Leftrightarrow & \color{blue}{15} .(\frac{180}{ \color{blue}{15} }x+ \frac{36}{ \color{blue}{15} })& = & (\frac{-75}{ \color{blue}{15} }x+ \frac{20}{ \color{blue}{15} }). \color{blue}{15} \\\Leftrightarrow & 180x \color{red}{+36} & = & \color{red}{-75x} +20 \\\Leftrightarrow & 180x \color{red}{+36} \color{blue}{-36} \color{blue}{+75x} & = & \color{red}{-75x} +20 \color{blue}{+75x} \color{blue}{-36} \\\Leftrightarrow & 180x+75x& = & 20-36 \\\Leftrightarrow & \color{red}{255} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{255} & & \\ & V = \left\{ \frac{-16}{255} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (4x+\frac{5}{3})& = & 3x+\frac{8}{3} \\\Leftrightarrow & 16x+\frac{20}{3}& = & 3x+\frac{8}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{48}{ \color{blue}{3} }x+ \frac{20}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{8}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 48x \color{red}{+20} & = & \color{red}{9x} +8 \\\Leftrightarrow & 48x \color{red}{+20} \color{blue}{-20} \color{blue}{-9x} & = & \color{red}{9x} +8 \color{blue}{-9x} \color{blue}{-20} \\\Leftrightarrow & 48x-9x& = & 8-20 \\\Leftrightarrow & \color{red}{39} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{39} & & \\\Leftrightarrow & x = \frac{-4}{13} & & \\ & V = \left\{ \frac{-4}{13} \right\} & \\\end{align}\)