Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{3})& = & -3x+\frac{3}{7} \\\Leftrightarrow & 14x-\frac{28}{3}& = & -3x+\frac{3}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{294}{ \color{blue}{21} }x- \frac{196}{ \color{blue}{21} })& = & (\frac{-63}{ \color{blue}{21} }x+ \frac{9}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & 294x \color{red}{-196} & = & \color{red}{-63x} +9 \\\Leftrightarrow & 294x \color{red}{-196} \color{blue}{+196} \color{blue}{+63x} & = & \color{red}{-63x} +9 \color{blue}{+63x} \color{blue}{+196} \\\Leftrightarrow & 294x+63x& = & 9+196 \\\Leftrightarrow & \color{red}{357} x& = & 205 \\\Leftrightarrow & x = \frac{205}{357} & & \\ & V = \left\{ \frac{205}{357} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (2x+\frac{5}{12})& = & 7x+\frac{7}{2} \\\Leftrightarrow & -10x-\frac{25}{12}& = & 7x+\frac{7}{2} \\ & & & \text{kgv van noemers 12 en 2 is 12} \\\Leftrightarrow & \color{blue}{12} .(\frac{-120}{ \color{blue}{12} }x- \frac{25}{ \color{blue}{12} })& = & (\frac{84}{ \color{blue}{12} }x+ \frac{42}{ \color{blue}{12} }). \color{blue}{12} \\\Leftrightarrow & -120x \color{red}{-25} & = & \color{red}{84x} +42 \\\Leftrightarrow & -120x \color{red}{-25} \color{blue}{+25} \color{blue}{-84x} & = & \color{red}{84x} +42 \color{blue}{-84x} \color{blue}{+25} \\\Leftrightarrow & -120x-84x& = & 42+25 \\\Leftrightarrow & \color{red}{-204} x& = & 67 \\\Leftrightarrow & x = \frac{67}{-204} & & \\\Leftrightarrow & x = \frac{-67}{204} & & \\ & V = \left\{ \frac{-67}{204} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (2x+\frac{2}{7})& = & 5x+\frac{7}{9} \\\Leftrightarrow & 12x+\frac{12}{7}& = & 5x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{756}{ \color{blue}{63} }x+ \frac{108}{ \color{blue}{63} })& = & (\frac{315}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & 756x \color{red}{+108} & = & \color{red}{315x} +49 \\\Leftrightarrow & 756x \color{red}{+108} \color{blue}{-108} \color{blue}{-315x} & = & \color{red}{315x} +49 \color{blue}{-315x} \color{blue}{-108} \\\Leftrightarrow & 756x-315x& = & 49-108 \\\Leftrightarrow & \color{red}{441} x& = & -59 \\\Leftrightarrow & x = \frac{-59}{441} & & \\ & V = \left\{ \frac{-59}{441} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (4x-\frac{4}{7})& = & -7x+\frac{3}{2} \\\Leftrightarrow & -16x+\frac{16}{7}& = & -7x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-224}{ \color{blue}{14} }x+ \frac{32}{ \color{blue}{14} })& = & (\frac{-98}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -224x \color{red}{+32} & = & \color{red}{-98x} +21 \\\Leftrightarrow & -224x \color{red}{+32} \color{blue}{-32} \color{blue}{+98x} & = & \color{red}{-98x} +21 \color{blue}{+98x} \color{blue}{-32} \\\Leftrightarrow & -224x+98x& = & 21-32 \\\Leftrightarrow & \color{red}{-126} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-126} & & \\\Leftrightarrow & x = \frac{11}{126} & & \\ & V = \left\{ \frac{11}{126} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (-2x-\frac{2}{5})& = & -5x+\frac{5}{11} \\\Leftrightarrow & 4x+\frac{4}{5}& = & -5x+\frac{5}{11} \\ & & & \text{kgv van noemers 5 en 11 is 55} \\\Leftrightarrow & \color{blue}{55} .(\frac{220}{ \color{blue}{55} }x+ \frac{44}{ \color{blue}{55} })& = & (\frac{-275}{ \color{blue}{55} }x+ \frac{25}{ \color{blue}{55} }). \color{blue}{55} \\\Leftrightarrow & 220x \color{red}{+44} & = & \color{red}{-275x} +25 \\\Leftrightarrow & 220x \color{red}{+44} \color{blue}{-44} \color{blue}{+275x} & = & \color{red}{-275x} +25 \color{blue}{+275x} \color{blue}{-44} \\\Leftrightarrow & 220x+275x& = & 25-44 \\\Leftrightarrow & \color{red}{495} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{495} & & \\ & V = \left\{ \frac{-19}{495} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-5x-\frac{1}{3})& = & -2x+\frac{10}{3} \\\Leftrightarrow & 35x+\frac{7}{3}& = & -2x+\frac{10}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{105}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} })& = & (\frac{-6}{ \color{blue}{3} }x+ \frac{10}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & 105x \color{red}{+7} & = & \color{red}{-6x} +10 \\\Leftrightarrow & 105x \color{red}{+7} \color{blue}{-7} \color{blue}{+6x} & = & \color{red}{-6x} +10 \color{blue}{+6x} \color{blue}{-7} \\\Leftrightarrow & 105x+6x& = & 10-7 \\\Leftrightarrow & \color{red}{111} x& = & 3 \\\Leftrightarrow & x = \frac{3}{111} & & \\\Leftrightarrow & x = \frac{1}{37} & & \\ & V = \left\{ \frac{1}{37} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (4x+\frac{3}{7})& = & -5x+\frac{5}{2} \\\Leftrightarrow & 12x+\frac{9}{7}& = & -5x+\frac{5}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{168}{ \color{blue}{14} }x+ \frac{18}{ \color{blue}{14} })& = & (\frac{-70}{ \color{blue}{14} }x+ \frac{35}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & 168x \color{red}{+18} & = & \color{red}{-70x} +35 \\\Leftrightarrow & 168x \color{red}{+18} \color{blue}{-18} \color{blue}{+70x} & = & \color{red}{-70x} +35 \color{blue}{+70x} \color{blue}{-18} \\\Leftrightarrow & 168x+70x& = & 35-18 \\\Leftrightarrow & \color{red}{238} x& = & 17 \\\Leftrightarrow & x = \frac{17}{238} & & \\\Leftrightarrow & x = \frac{1}{14} & & \\ & V = \left\{ \frac{1}{14} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{6} (3x-\frac{2}{5})& = & 5x+\frac{6}{7} \\\Leftrightarrow & 18x-\frac{12}{5}& = & 5x+\frac{6}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{630}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{30}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 630x \color{red}{-84} & = & \color{red}{175x} +30 \\\Leftrightarrow & 630x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +30 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 630x-175x& = & 30+84 \\\Leftrightarrow & \color{red}{455} x& = & 114 \\\Leftrightarrow & x = \frac{114}{455} & & \\ & V = \left\{ \frac{114}{455} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (-2x-\frac{4}{3})& = & -9x+\frac{8}{9} \\\Leftrightarrow & 14x+\frac{28}{3}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 3 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x+ \frac{84}{ \color{blue}{9} })& = & (\frac{-81}{ \color{blue}{9} }x+ \frac{8}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{+84} & = & \color{red}{-81x} +8 \\\Leftrightarrow & 126x \color{red}{+84} \color{blue}{-84} \color{blue}{+81x} & = & \color{red}{-81x} +8 \color{blue}{+81x} \color{blue}{-84} \\\Leftrightarrow & 126x+81x& = & 8-84 \\\Leftrightarrow & \color{red}{207} x& = & -76 \\\Leftrightarrow & x = \frac{-76}{207} & & \\ & V = \left\{ \frac{-76}{207} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (5x-\frac{5}{7})& = & -7x+\frac{6}{11} \\\Leftrightarrow & 10x-\frac{10}{7}& = & -7x+\frac{6}{11} \\ & & & \text{kgv van noemers 7 en 11 is 77} \\\Leftrightarrow & \color{blue}{77} .(\frac{770}{ \color{blue}{77} }x- \frac{110}{ \color{blue}{77} })& = & (\frac{-539}{ \color{blue}{77} }x+ \frac{42}{ \color{blue}{77} }). \color{blue}{77} \\\Leftrightarrow & 770x \color{red}{-110} & = & \color{red}{-539x} +42 \\\Leftrightarrow & 770x \color{red}{-110} \color{blue}{+110} \color{blue}{+539x} & = & \color{red}{-539x} +42 \color{blue}{+539x} \color{blue}{+110} \\\Leftrightarrow & 770x+539x& = & 42+110 \\\Leftrightarrow & \color{red}{1309} x& = & 152 \\\Leftrightarrow & x = \frac{152}{1309} & & \\ & V = \left\{ \frac{152}{1309} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-3} (-5x+\frac{4}{5})& = & -4x+\frac{4}{5} \\\Leftrightarrow & 15x-\frac{12}{5}& = & -4x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{75}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-20}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 75x \color{red}{-12} & = & \color{red}{-20x} +4 \\\Leftrightarrow & 75x \color{red}{-12} \color{blue}{+12} \color{blue}{+20x} & = & \color{red}{-20x} +4 \color{blue}{+20x} \color{blue}{+12} \\\Leftrightarrow & 75x+20x& = & 4+12 \\\Leftrightarrow & \color{red}{95} x& = & 16 \\\Leftrightarrow & x = \frac{16}{95} & & \\ & V = \left\{ \frac{16}{95} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (2x-\frac{3}{5})& = & -9x+\frac{9}{2} \\\Leftrightarrow & -8x+\frac{12}{5}& = & -9x+\frac{9}{2} \\ & & & \text{kgv van noemers 5 en 2 is 10} \\\Leftrightarrow & \color{blue}{10} .(\frac{-80}{ \color{blue}{10} }x+ \frac{24}{ \color{blue}{10} })& = & (\frac{-90}{ \color{blue}{10} }x+ \frac{45}{ \color{blue}{10} }). \color{blue}{10} \\\Leftrightarrow & -80x \color{red}{+24} & = & \color{red}{-90x} +45 \\\Leftrightarrow & -80x \color{red}{+24} \color{blue}{-24} \color{blue}{+90x} & = & \color{red}{-90x} +45 \color{blue}{+90x} \color{blue}{-24} \\\Leftrightarrow & -80x+90x& = & 45-24 \\\Leftrightarrow & \color{red}{10} x& = & 21 \\\Leftrightarrow & x = \frac{21}{10} & & \\ & V = \left\{ \frac{21}{10} \right\} & \\\end{align}\)