Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-4x-\frac{3}{7})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{616}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} })& = & (\frac{-231}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 616x \color{red}{+66} & = & \color{red}{-231x} +42 \\\Leftrightarrow & 616x \color{red}{+66} \color{blue}{-66} \color{blue}{+231x} & = & \color{red}{-231x} +42 \color{blue}{+231x} \color{blue}{-66} \\\Leftrightarrow & 616x+231x& = & 42-66 \\\Leftrightarrow & \color{red}{847} x& = & -24 \\\Leftrightarrow & x = \frac{-24}{847} & & \\ & V = \left\{ \frac{-24}{847} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{5}{8})& = & -7x+\frac{2}{5} \\\Leftrightarrow & 15x+\frac{15}{8}& = & -7x+\frac{2}{5} \\ & & & \text{kgv van noemers 8 en 5 is 40} \\\Leftrightarrow & \color{blue}{40} .(\frac{600}{ \color{blue}{40} }x+ \frac{75}{ \color{blue}{40} })& = & (\frac{-280}{ \color{blue}{40} }x+ \frac{16}{ \color{blue}{40} }). \color{blue}{40} \\\Leftrightarrow & 600x \color{red}{+75} & = & \color{red}{-280x} +16 \\\Leftrightarrow & 600x \color{red}{+75} \color{blue}{-75} \color{blue}{+280x} & = & \color{red}{-280x} +16 \color{blue}{+280x} \color{blue}{-75} \\\Leftrightarrow & 600x+280x& = & 16-75 \\\Leftrightarrow & \color{red}{880} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{880} & & \\ & V = \left\{ \frac{-59}{880} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x-\frac{3}{10})& = & 4x+\frac{4}{3} \\\Leftrightarrow & 15x+\frac{9}{10}& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 10 en 3 is 30} \\\Leftrightarrow & \color{blue}{30} .(\frac{450}{ \color{blue}{30} }x+ \frac{27}{ \color{blue}{30} })& = & (\frac{120}{ \color{blue}{30} }x+ \frac{40}{ \color{blue}{30} }). \color{blue}{30} \\\Leftrightarrow & 450x \color{red}{+27} & = & \color{red}{120x} +40 \\\Leftrightarrow & 450x \color{red}{+27} \color{blue}{-27} \color{blue}{-120x} & = & \color{red}{120x} +40 \color{blue}{-120x} \color{blue}{-27} \\\Leftrightarrow & 450x-120x& = & 40-27 \\\Leftrightarrow & \color{red}{330} x& = & 13 \\\Leftrightarrow & x = \frac{13}{330} & & \\ & V = \left\{ \frac{13}{330} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{2}{3})& = & -3x+\frac{3}{4} \\\Leftrightarrow & 35x-\frac{14}{3}& = & -3x+\frac{3}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{420}{ \color{blue}{12} }x- \frac{56}{ \color{blue}{12} })& = & (\frac{-36}{ \color{blue}{12} }x+ \frac{9}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & 420x \color{red}{-56} & = & \color{red}{-36x} +9 \\\Leftrightarrow & 420x \color{red}{-56} \color{blue}{+56} \color{blue}{+36x} & = & \color{red}{-36x} +9 \color{blue}{+36x} \color{blue}{+56} \\\Leftrightarrow & 420x+36x& = & 9+56 \\\Leftrightarrow & \color{red}{456} x& = & 65 \\\Leftrightarrow & x = \frac{65}{456} & & \\ & V = \left\{ \frac{65}{456} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-3x+\frac{4}{5})& = & -5x+\frac{7}{10} \\\Leftrightarrow & -9x+\frac{12}{5}& = & -5x+\frac{7}{10} \\ & & & \text{kgv van noemers 5 en 10 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-90}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-50}{ \color{blue}{10} }x+ \frac{7}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -90x \color{red}{+24} & = & \color{red}{-50x} +7 \\\Leftrightarrow & -90x \color{red}{+24} \color{blue}{-24} \color{blue}{+50x} & = & \color{red}{-50x} +7 \color{blue}{+50x} \color{blue}{-24} \\\Leftrightarrow & -90x+50x& = & 7-24 \\\Leftrightarrow & \color{red}{-40} x& = & -17 \\\Leftrightarrow & x = \frac{-17}{-40} & & \\\Leftrightarrow & x = \frac{17}{40} & & \\ & V = \left\{ \frac{17}{40} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (4x-\frac{4}{7})& = & 7x+\frac{7}{4} \\\Leftrightarrow & -20x+\frac{20}{7}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-560}{ \color{blue}{28} }x+ \frac{80}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{49}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -560x \color{red}{+80} & = & \color{red}{196x} +49 \\\Leftrightarrow & -560x \color{red}{+80} \color{blue}{-80} \color{blue}{-196x} & = & \color{red}{196x} +49 \color{blue}{-196x} \color{blue}{-80} \\\Leftrightarrow & -560x-196x& = & 49-80 \\\Leftrightarrow & \color{red}{-756} x& = & -31 \\\Leftrightarrow & x = \frac{-31}{-756} & & \\\Leftrightarrow & x = \frac{31}{756} & & \\ & V = \left\{ \frac{31}{756} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-2x+\frac{3}{10})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 6x-\frac{9}{10}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 10 en 9 is 90} \\\Leftrightarrow & \color{blue}{90} .(\frac{540}{ \color{blue}{90} }x- \frac{81}{ \color{blue}{90} })& = & (\frac{-630}{ \color{blue}{90} }x+ \frac{40}{ \color{blue}{90} }). \color{blue}{90} \\\Leftrightarrow & 540x \color{red}{-81} & = & \color{red}{-630x} +40 \\\Leftrightarrow & 540x \color{red}{-81} \color{blue}{+81} \color{blue}{+630x} & = & \color{red}{-630x} +40 \color{blue}{+630x} \color{blue}{+81} \\\Leftrightarrow & 540x+630x& = & 40+81 \\\Leftrightarrow & \color{red}{1170} x& = & 121 \\\Leftrightarrow & x = \frac{121}{1170} & & \\ & V = \left\{ \frac{121}{1170} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x-\frac{3}{2})& = & -7x+\frac{6}{5} \\\Leftrightarrow & -10x-\frac{15}{2}& = & -7x+\frac{6}{5} \\ & & & \text{kgv van noemers 2 en 5 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-100}{ \color{blue}{10} }x- \frac{75}{ \color{blue}{10} })& = & (\frac{-70}{ \color{blue}{10} }x+ \frac{12}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -100x \color{red}{-75} & = & \color{red}{-70x} +12 \\\Leftrightarrow & -100x \color{red}{-75} \color{blue}{+75} \color{blue}{+70x} & = & \color{red}{-70x} +12 \color{blue}{+70x} \color{blue}{+75} \\\Leftrightarrow & -100x+70x& = & 12+75 \\\Leftrightarrow & \color{red}{-30} x& = & 87 \\\Leftrightarrow & x = \frac{87}{-30} & & \\\Leftrightarrow & x = \frac{-29}{10} & & \\ & V = \left\{ \frac{-29}{10} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (3x+\frac{5}{3})& = & 8x+\frac{9}{4} \\\Leftrightarrow & -21x-\frac{35}{3}& = & 8x+\frac{9}{4} \\ & & & \text{kgv van noemers 3 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x- \frac{140}{ \color{blue}{12} })& = & (\frac{96}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{-140} & = & \color{red}{96x} +27 \\\Leftrightarrow & -252x \color{red}{-140} \color{blue}{+140} \color{blue}{-96x} & = & \color{red}{96x} +27 \color{blue}{-96x} \color{blue}{+140} \\\Leftrightarrow & -252x-96x& = & 27+140 \\\Leftrightarrow & \color{red}{-348} x& = & 167 \\\Leftrightarrow & x = \frac{167}{-348} & & \\\Leftrightarrow & x = \frac{-167}{348} & & \\ & V = \left\{ \frac{-167}{348} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x+\frac{2}{11})& = & 9x+\frac{8}{9} \\\Leftrightarrow & 10x+\frac{4}{11}& = & 9x+\frac{8}{9} \\ & & & \text{kgv van noemers 11 en 9 is 99} \\\Leftrightarrow & \color{blue}{99} .(\frac{990}{ \color{blue}{99} }x+ \frac{36}{ \color{blue}{99} })& = & (\frac{891}{ \color{blue}{99} }x+ \frac{88}{ \color{blue}{99} }). \color{blue}{99} \\\Leftrightarrow & 990x \color{red}{+36} & = & \color{red}{891x} +88 \\\Leftrightarrow & 990x \color{red}{+36} \color{blue}{-36} \color{blue}{-891x} & = & \color{red}{891x} +88 \color{blue}{-891x} \color{blue}{-36} \\\Leftrightarrow & 990x-891x& = & 88-36 \\\Leftrightarrow & \color{red}{99} x& = & 52 \\\Leftrightarrow & x = \frac{52}{99} & & \\ & V = \left\{ \frac{52}{99} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (2x-\frac{5}{6})& = & 3x+\frac{7}{2} \\\Leftrightarrow & 10x-\frac{25}{6}& = & 3x+\frac{7}{2} \\ & & & \text{kgv van noemers 6 en 2 is 6} \\\Leftrightarrow & \color{blue}{6} .(\frac{60}{ \color{blue}{6} }x- \frac{25}{ \color{blue}{6} })& = & (\frac{18}{ \color{blue}{6} }x+ \frac{21}{ \color{blue}{6} }). \color{blue}{6} \\\Leftrightarrow & 60x \color{red}{-25} & = & \color{red}{18x} +21 \\\Leftrightarrow & 60x \color{red}{-25} \color{blue}{+25} \color{blue}{-18x} & = & \color{red}{18x} +21 \color{blue}{-18x} \color{blue}{+25} \\\Leftrightarrow & 60x-18x& = & 21+25 \\\Leftrightarrow & \color{red}{42} x& = & 46 \\\Leftrightarrow & x = \frac{46}{42} & & \\\Leftrightarrow & x = \frac{23}{21} & & \\ & V = \left\{ \frac{23}{21} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-3x+\frac{5}{12})& = & -8x+\frac{9}{4} \\\Leftrightarrow & -21x+\frac{35}{12}& = & -8x+\frac{9}{4} \\ & & & \text{kgv van noemers 12 en 4 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-252}{ \color{blue}{12} }x+ \frac{35}{ \color{blue}{12} })& = & (\frac{-96}{ \color{blue}{12} }x+ \frac{27}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -252x \color{red}{+35} & = & \color{red}{-96x} +27 \\\Leftrightarrow & -252x \color{red}{+35} \color{blue}{-35} \color{blue}{+96x} & = & \color{red}{-96x} +27 \color{blue}{+96x} \color{blue}{-35} \\\Leftrightarrow & -252x+96x& = & 27-35 \\\Leftrightarrow & \color{red}{-156} x& = & -8 \\\Leftrightarrow & x = \frac{-8}{-156} & & \\\Leftrightarrow & x = \frac{2}{39} & & \\ & V = \left\{ \frac{2}{39} \right\} & \\\end{align}\)