Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{4}{3})& = & -8x+\frac{2}{11} \\\Leftrightarrow & 25x+\frac{20}{3}& = & -8x+\frac{2}{11} \\ & & & \text{kgv van noemers 3 en 11 is 33} \\\Leftrightarrow & \color{blue}{33} .(\frac{825}{ \color{blue}{33} }x+ \frac{220}{ \color{blue}{33} })& = & (\frac{-264}{ \color{blue}{33} }x+ \frac{6}{ \color{blue}{33} }). \color{blue}{33} \\\Leftrightarrow & 825x \color{red}{+220} & = & \color{red}{-264x} +6 \\\Leftrightarrow & 825x \color{red}{+220} \color{blue}{-220} \color{blue}{+264x} & = & \color{red}{-264x} +6 \color{blue}{+264x} \color{blue}{-220} \\\Leftrightarrow & 825x+264x& = & 6-220 \\\Leftrightarrow & \color{red}{1089} x& = & -214 \\\Leftrightarrow & x = \frac{-214}{1089} & & \\ & V = \left\{ \frac{-214}{1089} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-4x+\frac{2}{7})& = & -3x+\frac{8}{9} \\\Leftrightarrow & -8x+\frac{4}{7}& = & -3x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{36}{ \color{blue}{63} })& = & (\frac{-189}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+36} & = & \color{red}{-189x} +56 \\\Leftrightarrow & -504x \color{red}{+36} \color{blue}{-36} \color{blue}{+189x} & = & \color{red}{-189x} +56 \color{blue}{+189x} \color{blue}{-36} \\\Leftrightarrow & -504x+189x& = & 56-36 \\\Leftrightarrow & \color{red}{-315} x& = & 20 \\\Leftrightarrow & x = \frac{20}{-315} & & \\\Leftrightarrow & x = \frac{-4}{63} & & \\ & V = \left\{ \frac{-4}{63} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (5x-\frac{3}{5})& = & -7x+\frac{4}{9} \\\Leftrightarrow & 30x-\frac{18}{5}& = & -7x+\frac{4}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{1350}{ \color{blue}{45} }x- \frac{162}{ \color{blue}{45} })& = & (\frac{-315}{ \color{blue}{45} }x+ \frac{20}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 1350x \color{red}{-162} & = & \color{red}{-315x} +20 \\\Leftrightarrow & 1350x \color{red}{-162} \color{blue}{+162} \color{blue}{+315x} & = & \color{red}{-315x} +20 \color{blue}{+315x} \color{blue}{+162} \\\Leftrightarrow & 1350x+315x& = & 20+162 \\\Leftrightarrow & \color{red}{1665} x& = & 182 \\\Leftrightarrow & x = \frac{182}{1665} & & \\ & V = \left\{ \frac{182}{1665} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x+\frac{2}{3})& = & 9x+\frac{8}{7} \\\Leftrightarrow & 14x-\frac{14}{3}& = & 9x+\frac{8}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{294}{ \color{blue}{21} }x- \frac{98}{ \color{blue}{21} })& = & (\frac{189}{ \color{blue}{21} }x+ \frac{24}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 294x \color{red}{-98} & = & \color{red}{189x} +24 \\\Leftrightarrow & 294x \color{red}{-98} \color{blue}{+98} \color{blue}{-189x} & = & \color{red}{189x} +24 \color{blue}{-189x} \color{blue}{+98} \\\Leftrightarrow & 294x-189x& = & 24+98 \\\Leftrightarrow & \color{red}{105} x& = & 122 \\\Leftrightarrow & x = \frac{122}{105} & & \\ & V = \left\{ \frac{122}{105} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-2x+\frac{3}{7})& = & -7x+\frac{4}{3} \\\Leftrightarrow & -6x+\frac{9}{7}& = & -7x+\frac{4}{3} \\ & & & \text{kgv van noemers 7 en 3 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-126}{ \color{blue}{21} }x+ \frac{27}{ \color{blue}{21} })& = & (\frac{-147}{ \color{blue}{21} }x+ \frac{28}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -126x \color{red}{+27} & = & \color{red}{-147x} +28 \\\Leftrightarrow & -126x \color{red}{+27} \color{blue}{-27} \color{blue}{+147x} & = & \color{red}{-147x} +28 \color{blue}{+147x} \color{blue}{-27} \\\Leftrightarrow & -126x+147x& = & 28-27 \\\Leftrightarrow & \color{red}{21} x& = & 1 \\\Leftrightarrow & x = \frac{1}{21} & & \\ & V = \left\{ \frac{1}{21} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-2x+\frac{5}{3})& = & -5x+\frac{7}{8} \\\Leftrightarrow & -4x+\frac{10}{3}& = & -5x+\frac{7}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-96}{ \color{blue}{24} }x+ \frac{80}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{21}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -96x \color{red}{+80} & = & \color{red}{-120x} +21 \\\Leftrightarrow & -96x \color{red}{+80} \color{blue}{-80} \color{blue}{+120x} & = & \color{red}{-120x} +21 \color{blue}{+120x} \color{blue}{-80} \\\Leftrightarrow & -96x+120x& = & 21-80 \\\Leftrightarrow & \color{red}{24} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{24} & & \\ & V = \left\{ \frac{-59}{24} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{7})& = & 7x+\frac{3}{4} \\\Leftrightarrow & -10x+\frac{4}{7}& = & 7x+\frac{3}{4} \\ & & & \text{kgv van noemers 7 en 4 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{-280}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} })& = & (\frac{196}{ \color{blue}{28} }x+ \frac{21}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & -280x \color{red}{+16} & = & \color{red}{196x} +21 \\\Leftrightarrow & -280x \color{red}{+16} \color{blue}{-16} \color{blue}{-196x} & = & \color{red}{196x} +21 \color{blue}{-196x} \color{blue}{-16} \\\Leftrightarrow & -280x-196x& = & 21-16 \\\Leftrightarrow & \color{red}{-476} x& = & 5 \\\Leftrightarrow & x = \frac{5}{-476} & & \\\Leftrightarrow & x = \frac{-5}{476} & & \\ & V = \left\{ \frac{-5}{476} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x+\frac{5}{3})& = & 3x+\frac{10}{3} \\\Leftrightarrow & 35x-\frac{35}{3}& = & 3x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x- \frac{35}{ \color{blue}{3} })& = & (\frac{9}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{-35} & = & \color{red}{9x} +10 \\\Leftrightarrow & 105x \color{red}{-35} \color{blue}{+35} \color{blue}{-9x} & = & \color{red}{9x} +10 \color{blue}{-9x} \color{blue}{+35} \\\Leftrightarrow & 105x-9x& = & 10+35 \\\Leftrightarrow & \color{red}{96} x& = & 45 \\\Leftrightarrow & x = \frac{45}{96} & & \\\Leftrightarrow & x = \frac{15}{32} & & \\ & V = \left\{ \frac{15}{32} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (4x+\frac{3}{7})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 8x+\frac{6}{7}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 7 en 7 is 7} \\\Leftrightarrow & \color{blue}{7} .(\frac{56}{ \color{blue}{7} }x+ \frac{6}{ \color{blue}{7} })& = & (\frac{-21}{ \color{blue}{7} }x+ \frac{3}{ \color{blue}{7} }). \color{blue}{7} \\\Leftrightarrow & 56x \color{red}{+6} & = & \color{red}{-21x} +3 \\\Leftrightarrow & 56x \color{red}{+6} \color{blue}{-6} \color{blue}{+21x} & = & \color{red}{-21x} +3 \color{blue}{+21x} \color{blue}{-6} \\\Leftrightarrow & 56x+21x& = & 3-6 \\\Leftrightarrow & \color{red}{77} x& = & -3 \\\Leftrightarrow & x = \frac{-3}{77} & & \\ & V = \left\{ \frac{-3}{77} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (-2x-\frac{5}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & -12x-\frac{30}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-168}{ \color{blue}{14} }x- \frac{60}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -168x \color{red}{-60} & = & \color{red}{-70x} +35 \\\Leftrightarrow & -168x \color{red}{-60} \color{blue}{+60} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{+60} \\\Leftrightarrow & -168x+70x& = & 35+60 \\\Leftrightarrow & \color{red}{-98} x& = & 95 \\\Leftrightarrow & x = \frac{95}{-98} & & \\\Leftrightarrow & x = \frac{-95}{98} & & \\ & V = \left\{ \frac{-95}{98} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x-\frac{5}{4})& = & -3x+\frac{6}{11} \\\Leftrightarrow & 25x+\frac{25}{4}& = & -3x+\frac{6}{11} \\ & & & \text{kgv van noemers 4 en 11 is 44} \\\Leftrightarrow & \color{blue}{44} .(\frac{1100}{ \color{blue}{44} }x+ \frac{275}{ \color{blue}{44} })& = & (\frac{-132}{ \color{blue}{44} }x+ \frac{24}{ \color{blue}{44} }). \color{blue}{44} \\\Leftrightarrow & 1100x \color{red}{+275} & = & \color{red}{-132x} +24 \\\Leftrightarrow & 1100x \color{red}{+275} \color{blue}{-275} \color{blue}{+132x} & = & \color{red}{-132x} +24 \color{blue}{+132x} \color{blue}{-275} \\\Leftrightarrow & 1100x+132x& = & 24-275 \\\Leftrightarrow & \color{red}{1232} x& = & -251 \\\Leftrightarrow & x = \frac{-251}{1232} & & \\ & V = \left\{ \frac{-251}{1232} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (5x-\frac{2}{11})& = & -2x+\frac{6}{7} \\\Leftrightarrow & 25x-\frac{10}{11}& = & -2x+\frac{6}{7} \\ & & & \text{kgv van noemers 11 en 7 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{1925}{ \color{blue}{77} }x- \frac{70}{ \color{blue}{77} })& = & (\frac{-154}{ \color{blue}{77} }x+ \frac{66}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 1925x \color{red}{-70} & = & \color{red}{-154x} +66 \\\Leftrightarrow & 1925x \color{red}{-70} \color{blue}{+70} \color{blue}{+154x} & = & \color{red}{-154x} +66 \color{blue}{+154x} \color{blue}{+70} \\\Leftrightarrow & 1925x+154x& = & 66+70 \\\Leftrightarrow & \color{red}{2079} x& = & 136 \\\Leftrightarrow & x = \frac{136}{2079} & & \\ & V = \left\{ \frac{136}{2079} \right\} & \\\end{align}\)