Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-3x+\frac{2}{7})& = & -8x+\frac{8}{9} \\\Leftrightarrow & 15x-\frac{10}{7}& = & -8x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{945}{ \color{blue}{63} }x- \frac{90}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 945x \color{red}{-90} & = & \color{red}{-504x} +56 \\\Leftrightarrow & 945x \color{red}{-90} \color{blue}{+90} \color{blue}{+504x} & = & \color{red}{-504x} +56 \color{blue}{+504x} \color{blue}{+90} \\\Leftrightarrow & 945x+504x& = & 56+90 \\\Leftrightarrow & \color{red}{1449} x& = & 146 \\\Leftrightarrow & x = \frac{146}{1449} & & \\ & V = \left\{ \frac{146}{1449} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x-\frac{3}{4})& = & -7x+\frac{5}{11} \\\Leftrightarrow & -10x+\frac{15}{4}& = & -7x+\frac{5}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{-440}{ \color{blue}{44} }x+ \frac{165}{ \color{blue}{44} })& = & (\frac{-308}{ \color{blue}{44} }x+ \frac{20}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & -440x \color{red}{+165} & = & \color{red}{-308x} +20 \\\Leftrightarrow & -440x \color{red}{+165} \color{blue}{-165} \color{blue}{+308x} & = & \color{red}{-308x} +20 \color{blue}{+308x} \color{blue}{-165} \\\Leftrightarrow & -440x+308x& = & 20-165 \\\Leftrightarrow & \color{red}{-132} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-132} & & \\\Leftrightarrow & x = \frac{145}{132} & & \\ & V = \left\{ \frac{145}{132} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{5})& = & 5x+\frac{7}{6} \\\Leftrightarrow & 6x-\frac{9}{5}& = & 5x+\frac{7}{6} \\ & & & \text{kgv van noemers 5 en 6 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{180}{ \color{blue}{30} }x- \frac{54}{ \color{blue}{30} })& = & (\frac{150}{ \color{blue}{30} }x+ \frac{35}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 180x \color{red}{-54} & = & \color{red}{150x} +35 \\\Leftrightarrow & 180x \color{red}{-54} \color{blue}{+54} \color{blue}{-150x} & = & \color{red}{150x} +35 \color{blue}{-150x} \color{blue}{+54} \\\Leftrightarrow & 180x-150x& = & 35+54 \\\Leftrightarrow & \color{red}{30} x& = & 89 \\\Leftrightarrow & x = \frac{89}{30} & & \\ & V = \left\{ \frac{89}{30} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x+\frac{5}{7})& = & -9x+\frac{2}{11} \\\Leftrightarrow & 4x-\frac{10}{7}& = & -9x+\frac{2}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{308}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-693}{ \color{blue}{77} }x+ \frac{14}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 308x \color{red}{-110} & = & \color{red}{-693x} +14 \\\Leftrightarrow & 308x \color{red}{-110} \color{blue}{+110} \color{blue}{+693x} & = & \color{red}{-693x} +14 \color{blue}{+693x} \color{blue}{+110} \\\Leftrightarrow & 308x+693x& = & 14+110 \\\Leftrightarrow & \color{red}{1001} x& = & 124 \\\Leftrightarrow & x = \frac{124}{1001} & & \\ & V = \left\{ \frac{124}{1001} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-4x+\frac{4}{5})& = & -5x+\frac{9}{5} \\\Leftrightarrow & -24x+\frac{24}{5}& = & -5x+\frac{9}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-120}{ \color{blue}{5} }x+ \frac{24}{ \color{blue}{5} })& = & (\frac{-25}{ \color{blue}{5} }x+ \frac{9}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -120x \color{red}{+24} & = & \color{red}{-25x} +9 \\\Leftrightarrow & -120x \color{red}{+24} \color{blue}{-24} \color{blue}{+25x} & = & \color{red}{-25x} +9 \color{blue}{+25x} \color{blue}{-24} \\\Leftrightarrow & -120x+25x& = & 9-24 \\\Leftrightarrow & \color{red}{-95} x& = & -15 \\\Leftrightarrow & x = \frac{-15}{-95} & & \\\Leftrightarrow & x = \frac{3}{19} & & \\ & V = \left\{ \frac{3}{19} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{4}{11})& = & -9x+\frac{9}{5} \\\Leftrightarrow & 8x-\frac{16}{11}& = & -9x+\frac{9}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{440}{ \color{blue}{55} }x- \frac{80}{ \color{blue}{55} })& = & (\frac{-495}{ \color{blue}{55} }x+ \frac{99}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 440x \color{red}{-80} & = & \color{red}{-495x} +99 \\\Leftrightarrow & 440x \color{red}{-80} \color{blue}{+80} \color{blue}{+495x} & = & \color{red}{-495x} +99 \color{blue}{+495x} \color{blue}{+80} \\\Leftrightarrow & 440x+495x& = & 99+80 \\\Leftrightarrow & \color{red}{935} x& = & 179 \\\Leftrightarrow & x = \frac{179}{935} & & \\ & V = \left\{ \frac{179}{935} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{2}{5})& = & 5x+\frac{2}{11} \\\Leftrightarrow & -12x+\frac{6}{5}& = & 5x+\frac{2}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-660}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} })& = & (\frac{275}{ \color{blue}{55} }x+ \frac{10}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -660x \color{red}{+66} & = & \color{red}{275x} +10 \\\Leftrightarrow & -660x \color{red}{+66} \color{blue}{-66} \color{blue}{-275x} & = & \color{red}{275x} +10 \color{blue}{-275x} \color{blue}{-66} \\\Leftrightarrow & -660x-275x& = & 10-66 \\\Leftrightarrow & \color{red}{-935} x& = & -56 \\\Leftrightarrow & x = \frac{-56}{-935} & & \\\Leftrightarrow & x = \frac{56}{935} & & \\ & V = \left\{ \frac{56}{935} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (5x-\frac{3}{5})& = & 8x+\frac{4}{9} \\\Leftrightarrow & -15x+\frac{9}{5}& = & 8x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-675}{ \color{blue}{45} }x+ \frac{81}{ \color{blue}{45} })& = & (\frac{360}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -675x \color{red}{+81} & = & \color{red}{360x} +20 \\\Leftrightarrow & -675x \color{red}{+81} \color{blue}{-81} \color{blue}{-360x} & = & \color{red}{360x} +20 \color{blue}{-360x} \color{blue}{-81} \\\Leftrightarrow & -675x-360x& = & 20-81 \\\Leftrightarrow & \color{red}{-1035} x& = & -61 \\\Leftrightarrow & x = \frac{-61}{-1035} & & \\\Leftrightarrow & x = \frac{61}{1035} & & \\ & V = \left\{ \frac{61}{1035} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{2}{7})& = & -4x+\frac{2}{3} \\\Leftrightarrow & 25x+\frac{10}{7}& = & -4x+\frac{2}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{525}{ \color{blue}{21} }x+ \frac{30}{ \color{blue}{21} })& = & (\frac{-84}{ \color{blue}{21} }x+ \frac{14}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 525x \color{red}{+30} & = & \color{red}{-84x} +14 \\\Leftrightarrow & 525x \color{red}{+30} \color{blue}{-30} \color{blue}{+84x} & = & \color{red}{-84x} +14 \color{blue}{+84x} \color{blue}{-30} \\\Leftrightarrow & 525x+84x& = & 14-30 \\\Leftrightarrow & \color{red}{609} x& = & -16 \\\Leftrightarrow & x = \frac{-16}{609} & & \\ & V = \left\{ \frac{-16}{609} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (5x+\frac{4}{7})& = & 7x+\frac{3}{10} \\\Leftrightarrow & -30x-\frac{24}{7}& = & 7x+\frac{3}{10} \\ & & & \text{kgv van noemers 7 en 10 is 70} \\\Leftrightarrow & \color{blue}{70} .(\frac{-2100}{ \color{blue}{70} }x- \frac{240}{ \color{blue}{70} })& = & (\frac{490}{ \color{blue}{70} }x+ \frac{21}{ \color{blue}{70} }). \color{blue}{70} \\\Leftrightarrow & -2100x \color{red}{-240} & = & \color{red}{490x} +21 \\\Leftrightarrow & -2100x \color{red}{-240} \color{blue}{+240} \color{blue}{-490x} & = & \color{red}{490x} +21 \color{blue}{-490x} \color{blue}{+240} \\\Leftrightarrow & -2100x-490x& = & 21+240 \\\Leftrightarrow & \color{red}{-2590} x& = & 261 \\\Leftrightarrow & x = \frac{261}{-2590} & & \\\Leftrightarrow & x = \frac{-261}{2590} & & \\ & V = \left\{ \frac{-261}{2590} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-4x+\frac{5}{11})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 20x-\frac{25}{11}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 11 en 3 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{660}{ \color{blue}{33} }x- \frac{75}{ \color{blue}{33} })& = & (\frac{99}{ \color{blue}{33} }x+ \frac{110}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 660x \color{red}{-75} & = & \color{red}{99x} +110 \\\Leftrightarrow & 660x \color{red}{-75} \color{blue}{+75} \color{blue}{-99x} & = & \color{red}{99x} +110 \color{blue}{-99x} \color{blue}{+75} \\\Leftrightarrow & 660x-99x& = & 110+75 \\\Leftrightarrow & \color{red}{561} x& = & 185 \\\Leftrightarrow & x = \frac{185}{561} & & \\ & V = \left\{ \frac{185}{561} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-3x+\frac{4}{11})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -6x+\frac{8}{11}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 11 en 2 is 22} \\\Leftrightarrow & \color{blue}{22} .(\frac{-132}{ \color{blue}{22} }x+ \frac{16}{ \color{blue}{22} })& = & (\frac{154}{ \color{blue}{22} }x+ \frac{77}{ \color{blue}{22} }). \color{blue}{22} \\\Leftrightarrow & -132x \color{red}{+16} & = & \color{red}{154x} +77 \\\Leftrightarrow & -132x \color{red}{+16} \color{blue}{-16} \color{blue}{-154x} & = & \color{red}{154x} +77 \color{blue}{-154x} \color{blue}{-16} \\\Leftrightarrow & -132x-154x& = & 77-16 \\\Leftrightarrow & \color{red}{-286} x& = & 61 \\\Leftrightarrow & x = \frac{61}{-286} & & \\\Leftrightarrow & x = \frac{-61}{286} & & \\ & V = \left\{ \frac{-61}{286} \right\} & \\\end{align}\)