Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-3x+\frac{3}{4})& = & 8x+\frac{3}{4} \\\Leftrightarrow & -15x+\frac{15}{4}& = & 8x+\frac{3}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{-60}{ \color{blue}{4} }x+ \frac{15}{ \color{blue}{4} })& = & (\frac{32}{ \color{blue}{4} }x+ \frac{3}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & -60x \color{red}{+15} & = & \color{red}{32x} +3 \\\Leftrightarrow & -60x \color{red}{+15} \color{blue}{-15} \color{blue}{-32x} & = & \color{red}{32x} +3 \color{blue}{-32x} \color{blue}{-15} \\\Leftrightarrow & -60x-32x& = & 3-15 \\\Leftrightarrow & \color{red}{-92} x& = & -12 \\\Leftrightarrow & x = \frac{-12}{-92} & & \\\Leftrightarrow & x = \frac{3}{23} & & \\ & V = \left\{ \frac{3}{23} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{3}{8})& = & -3x+\frac{10}{9} \\\Leftrightarrow & -20x+\frac{15}{8}& = & -3x+\frac{10}{9} \\ & & & \text{kgv van noemers 8 en 9 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-1440}{ \color{blue}{72} }x+ \frac{135}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{80}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -1440x \color{red}{+135} & = & \color{red}{-216x} +80 \\\Leftrightarrow & -1440x \color{red}{+135} \color{blue}{-135} \color{blue}{+216x} & = & \color{red}{-216x} +80 \color{blue}{+216x} \color{blue}{-135} \\\Leftrightarrow & -1440x+216x& = & 80-135 \\\Leftrightarrow & \color{red}{-1224} x& = & -55 \\\Leftrightarrow & x = \frac{-55}{-1224} & & \\\Leftrightarrow & x = \frac{55}{1224} & & \\ & V = \left\{ \frac{55}{1224} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{5}{3})& = & -3x+\frac{4}{11} \\\Leftrightarrow & -8x+\frac{20}{3}& = & -3x+\frac{4}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{-264}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-99}{ \color{blue}{33} }x+ \frac{12}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & -264x \color{red}{+220} & = & \color{red}{-99x} +12 \\\Leftrightarrow & -264x \color{red}{+220} \color{blue}{-220} \color{blue}{+99x} & = & \color{red}{-99x} +12 \color{blue}{+99x} \color{blue}{-220} \\\Leftrightarrow & -264x+99x& = & 12-220 \\\Leftrightarrow & \color{red}{-165} x& = & -208 \\\Leftrightarrow & x = \frac{-208}{-165} & & \\\Leftrightarrow & x = \frac{208}{165} & & \\ & V = \left\{ \frac{208}{165} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x-\frac{4}{5})& = & -2x+\frac{2}{9} \\\Leftrightarrow & 9x-\frac{12}{5}& = & -2x+\frac{2}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{405}{ \color{blue}{45} }x- \frac{108}{ \color{blue}{45} })& = & (\frac{-90}{ \color{blue}{45} }x+ \frac{10}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 405x \color{red}{-108} & = & \color{red}{-90x} +10 \\\Leftrightarrow & 405x \color{red}{-108} \color{blue}{+108} \color{blue}{+90x} & = & \color{red}{-90x} +10 \color{blue}{+90x} \color{blue}{+108} \\\Leftrightarrow & 405x+90x& = & 10+108 \\\Leftrightarrow & \color{red}{495} x& = & 118 \\\Leftrightarrow & x = \frac{118}{495} & & \\ & V = \left\{ \frac{118}{495} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x+\frac{3}{8})& = & 3x+\frac{10}{3} \\\Leftrightarrow & -14x+\frac{21}{8}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 8 en 3 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-336}{ \color{blue}{24} }x+ \frac{63}{ \color{blue}{24} })& = & (\frac{72}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -336x \color{red}{+63} & = & \color{red}{72x} +80 \\\Leftrightarrow & -336x \color{red}{+63} \color{blue}{-63} \color{blue}{-72x} & = & \color{red}{72x} +80 \color{blue}{-72x} \color{blue}{-63} \\\Leftrightarrow & -336x-72x& = & 80-63 \\\Leftrightarrow & \color{red}{-408} x& = & 17 \\\Leftrightarrow & x = \frac{17}{-408} & & \\\Leftrightarrow & x = \frac{-1}{24} & & \\ & V = \left\{ \frac{-1}{24} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (4x+\frac{4}{7})& = & -5x+\frac{6}{11} \\\Leftrightarrow & -24x-\frac{24}{7}& = & -5x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{-1848}{ \color{blue}{77} }x- \frac{264}{ \color{blue}{77} })& = & (\frac{-385}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & -1848x \color{red}{-264} & = & \color{red}{-385x} +42 \\\Leftrightarrow & -1848x \color{red}{-264} \color{blue}{+264} \color{blue}{+385x} & = & \color{red}{-385x} +42 \color{blue}{+385x} \color{blue}{+264} \\\Leftrightarrow & -1848x+385x& = & 42+264 \\\Leftrightarrow & \color{red}{-1463} x& = & 306 \\\Leftrightarrow & x = \frac{306}{-1463} & & \\\Leftrightarrow & x = \frac{-306}{1463} & & \\ & V = \left\{ \frac{-306}{1463} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x+\frac{2}{5})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -18x-\frac{12}{5}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 5 en 4 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{-360}{ \color{blue}{20} }x- \frac{48}{ \color{blue}{20} })& = & (\frac{140}{ \color{blue}{20} }x+ \frac{15}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & -360x \color{red}{-48} & = & \color{red}{140x} +15 \\\Leftrightarrow & -360x \color{red}{-48} \color{blue}{+48} \color{blue}{-140x} & = & \color{red}{140x} +15 \color{blue}{-140x} \color{blue}{+48} \\\Leftrightarrow & -360x-140x& = & 15+48 \\\Leftrightarrow & \color{red}{-500} x& = & 63 \\\Leftrightarrow & x = \frac{63}{-500} & & \\\Leftrightarrow & x = \frac{-63}{500} & & \\ & V = \left\{ \frac{-63}{500} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{4}{3})& = & 7x+\frac{4}{3} \\\Leftrightarrow & 10x-\frac{20}{3}& = & 7x+\frac{4}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{30}{ \color{blue}{3} }x- \frac{20}{ \color{blue}{3} })& = & (\frac{21}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 30x \color{red}{-20} & = & \color{red}{21x} +4 \\\Leftrightarrow & 30x \color{red}{-20} \color{blue}{+20} \color{blue}{-21x} & = & \color{red}{21x} +4 \color{blue}{-21x} \color{blue}{+20} \\\Leftrightarrow & 30x-21x& = & 4+20 \\\Leftrightarrow & \color{red}{9} x& = & 24 \\\Leftrightarrow & x = \frac{24}{9} & & \\\Leftrightarrow & x = \frac{8}{3} & & \\ & V = \left\{ \frac{8}{3} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 4x+\frac{7}{10} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 4x+\frac{7}{10} \\ & & & \text{kgv van noemers 4 en 10 is 20} \\\Leftrightarrow & \color{blue}{20} .(\frac{500}{ \color{blue}{20} }x- \frac{75}{ \color{blue}{20} })& = & (\frac{80}{ \color{blue}{20} }x+ \frac{14}{ \color{blue}{20} }). \color{blue}{20} \\\Leftrightarrow & 500x \color{red}{-75} & = & \color{red}{80x} +14 \\\Leftrightarrow & 500x \color{red}{-75} \color{blue}{+75} \color{blue}{-80x} & = & \color{red}{80x} +14 \color{blue}{-80x} \color{blue}{+75} \\\Leftrightarrow & 500x-80x& = & 14+75 \\\Leftrightarrow & \color{red}{420} x& = & 89 \\\Leftrightarrow & x = \frac{89}{420} & & \\ & V = \left\{ \frac{89}{420} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{4}{7})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 10x+\frac{8}{7}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{630}{ \color{blue}{63} }x+ \frac{72}{ \color{blue}{63} })& = & (\frac{-441}{ \color{blue}{63} }x+ \frac{28}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 630x \color{red}{+72} & = & \color{red}{-441x} +28 \\\Leftrightarrow & 630x \color{red}{+72} \color{blue}{-72} \color{blue}{+441x} & = & \color{red}{-441x} +28 \color{blue}{+441x} \color{blue}{-72} \\\Leftrightarrow & 630x+441x& = & 28-72 \\\Leftrightarrow & \color{red}{1071} x& = & -44 \\\Leftrightarrow & x = \frac{-44}{1071} & & \\ & V = \left\{ \frac{-44}{1071} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{4}{11})& = & -5x+\frac{6}{5} \\\Leftrightarrow & 18x-\frac{24}{11}& = & -5x+\frac{6}{5} \\ & & & \text{kgv van noemers 11 en 5 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{990}{ \color{blue}{55} }x- \frac{120}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{66}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 990x \color{red}{-120} & = & \color{red}{-275x} +66 \\\Leftrightarrow & 990x \color{red}{-120} \color{blue}{+120} \color{blue}{+275x} & = & \color{red}{-275x} +66 \color{blue}{+275x} \color{blue}{+120} \\\Leftrightarrow & 990x+275x& = & 66+120 \\\Leftrightarrow & \color{red}{1265} x& = & 186 \\\Leftrightarrow & x = \frac{186}{1265} & & \\ & V = \left\{ \frac{186}{1265} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x-\frac{4}{5})& = & 9x+\frac{3}{11} \\\Leftrightarrow & -28x-\frac{28}{5}& = & 9x+\frac{3}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{-1540}{ \color{blue}{55} }x- \frac{308}{ \color{blue}{55} })& = & (\frac{495}{ \color{blue}{55} }x+ \frac{15}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & -1540x \color{red}{-308} & = & \color{red}{495x} +15 \\\Leftrightarrow & -1540x \color{red}{-308} \color{blue}{+308} \color{blue}{-495x} & = & \color{red}{495x} +15 \color{blue}{-495x} \color{blue}{+308} \\\Leftrightarrow & -1540x-495x& = & 15+308 \\\Leftrightarrow & \color{red}{-2035} x& = & 323 \\\Leftrightarrow & x = \frac{323}{-2035} & & \\\Leftrightarrow & x = \frac{-323}{2035} & & \\ & V = \left\{ \frac{-323}{2035} \right\} & \\\end{align}\)