Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x-\frac{5}{7})& = & -9x+\frac{8}{9} \\\Leftrightarrow & -8x+\frac{10}{7}& = & -9x+\frac{8}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-504}{ \color{blue}{63} }x+ \frac{90}{ \color{blue}{63} })& = & (\frac{-567}{ \color{blue}{63} }x+ \frac{56}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -504x \color{red}{+90} & = & \color{red}{-567x} +56 \\\Leftrightarrow & -504x \color{red}{+90} \color{blue}{-90} \color{blue}{+567x} & = & \color{red}{-567x} +56 \color{blue}{+567x} \color{blue}{-90} \\\Leftrightarrow & -504x+567x& = & 56-90 \\\Leftrightarrow & \color{red}{63} x& = & -34 \\\Leftrightarrow & x = \frac{-34}{63} & & \\ & V = \left\{ \frac{-34}{63} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (3x-\frac{4}{5})& = & -5x+\frac{5}{9} \\\Leftrightarrow & 12x-\frac{16}{5}& = & -5x+\frac{5}{9} \\ & & & \text{kgv van noemers 5 en 9 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{540}{ \color{blue}{45} }x- \frac{144}{ \color{blue}{45} })& = & (\frac{-225}{ \color{blue}{45} }x+ \frac{25}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & 540x \color{red}{-144} & = & \color{red}{-225x} +25 \\\Leftrightarrow & 540x \color{red}{-144} \color{blue}{+144} \color{blue}{+225x} & = & \color{red}{-225x} +25 \color{blue}{+225x} \color{blue}{+144} \\\Leftrightarrow & 540x+225x& = & 25+144 \\\Leftrightarrow & \color{red}{765} x& = & 169 \\\Leftrightarrow & x = \frac{169}{765} & & \\ & V = \left\{ \frac{169}{765} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (-4x+\frac{2}{9})& = & -5x+\frac{4}{9} \\\Leftrightarrow & 16x-\frac{8}{9}& = & -5x+\frac{4}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{144}{ \color{blue}{9} }x- \frac{8}{ \color{blue}{9} })& = & (\frac{-45}{ \color{blue}{9} }x+ \frac{4}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 144x \color{red}{-8} & = & \color{red}{-45x} +4 \\\Leftrightarrow & 144x \color{red}{-8} \color{blue}{+8} \color{blue}{+45x} & = & \color{red}{-45x} +4 \color{blue}{+45x} \color{blue}{+8} \\\Leftrightarrow & 144x+45x& = & 4+8 \\\Leftrightarrow & \color{red}{189} x& = & 12 \\\Leftrightarrow & x = \frac{12}{189} & & \\\Leftrightarrow & x = \frac{4}{63} & & \\ & V = \left\{ \frac{4}{63} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-4} (3x-\frac{5}{3})& = & -5x+\frac{5}{8} \\\Leftrightarrow & -12x+\frac{20}{3}& = & -5x+\frac{5}{8} \\ & & & \text{kgv van noemers 3 en 8 is 24} \\\Leftrightarrow & \color{blue}{24} .(\frac{-288}{ \color{blue}{24} }x+ \frac{160}{ \color{blue}{24} })& = & (\frac{-120}{ \color{blue}{24} }x+ \frac{15}{ \color{blue}{24} }). \color{blue}{24} \\\Leftrightarrow & -288x \color{red}{+160} & = & \color{red}{-120x} +15 \\\Leftrightarrow & -288x \color{red}{+160} \color{blue}{-160} \color{blue}{+120x} & = & \color{red}{-120x} +15 \color{blue}{+120x} \color{blue}{-160} \\\Leftrightarrow & -288x+120x& = & 15-160 \\\Leftrightarrow & \color{red}{-168} x& = & -145 \\\Leftrightarrow & x = \frac{-145}{-168} & & \\\Leftrightarrow & x = \frac{145}{168} & & \\ & V = \left\{ \frac{145}{168} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-2x-\frac{2}{9})& = & 3x+\frac{4}{5} \\\Leftrightarrow & -14x-\frac{14}{9}& = & 3x+\frac{4}{5} \\ & & & \text{kgv van noemers 9 en 5 is 45} \\\Leftrightarrow & \color{blue}{45} .(\frac{-630}{ \color{blue}{45} }x- \frac{70}{ \color{blue}{45} })& = & (\frac{135}{ \color{blue}{45} }x+ \frac{36}{ \color{blue}{45} }). \color{blue}{45} \\\Leftrightarrow & -630x \color{red}{-70} & = & \color{red}{135x} +36 \\\Leftrightarrow & -630x \color{red}{-70} \color{blue}{+70} \color{blue}{-135x} & = & \color{red}{135x} +36 \color{blue}{-135x} \color{blue}{+70} \\\Leftrightarrow & -630x-135x& = & 36+70 \\\Leftrightarrow & \color{red}{-765} x& = & 106 \\\Leftrightarrow & x = \frac{106}{-765} & & \\\Leftrightarrow & x = \frac{-106}{765} & & \\ & V = \left\{ \frac{-106}{765} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{4}{9})& = & -3x+\frac{7}{8} \\\Leftrightarrow & -35x+\frac{28}{9}& = & -3x+\frac{7}{8} \\ & & & \text{kgv van noemers 9 en 8 is 72} \\\Leftrightarrow & \color{blue}{72} .(\frac{-2520}{ \color{blue}{72} }x+ \frac{224}{ \color{blue}{72} })& = & (\frac{-216}{ \color{blue}{72} }x+ \frac{63}{ \color{blue}{72} }). \color{blue}{72} \\\Leftrightarrow & -2520x \color{red}{+224} & = & \color{red}{-216x} +63 \\\Leftrightarrow & -2520x \color{red}{+224} \color{blue}{-224} \color{blue}{+216x} & = & \color{red}{-216x} +63 \color{blue}{+216x} \color{blue}{-224} \\\Leftrightarrow & -2520x+216x& = & 63-224 \\\Leftrightarrow & \color{red}{-2304} x& = & -161 \\\Leftrightarrow & x = \frac{-161}{-2304} & & \\\Leftrightarrow & x = \frac{161}{2304} & & \\ & V = \left\{ \frac{161}{2304} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (3x-1)& = & 4x+\frac{4}{3} \\\Leftrightarrow & -15x+5& = & 4x+\frac{4}{3} \\ & & & \text{kgv van noemers 1 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-45}{ \color{blue}{3} }x+ \frac{15}{ \color{blue}{3} })& = & (\frac{12}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -45x \color{red}{+15} & = & \color{red}{12x} +4 \\\Leftrightarrow & -45x \color{red}{+15} \color{blue}{-15} \color{blue}{-12x} & = & \color{red}{12x} +4 \color{blue}{-12x} \color{blue}{-15} \\\Leftrightarrow & -45x-12x& = & 4-15 \\\Leftrightarrow & \color{red}{-57} x& = & -11 \\\Leftrightarrow & x = \frac{-11}{-57} & & \\\Leftrightarrow & x = \frac{11}{57} & & \\ & V = \left\{ \frac{11}{57} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-5x+\frac{3}{4})& = & 7x+\frac{7}{4} \\\Leftrightarrow & 25x-\frac{15}{4}& = & 7x+\frac{7}{4} \\ & & & \text{kgv van noemers 4 en 4 is 4} \\\Leftrightarrow & \color{blue}{4} .(\frac{100}{ \color{blue}{4} }x- \frac{15}{ \color{blue}{4} })& = & (\frac{28}{ \color{blue}{4} }x+ \frac{7}{ \color{blue}{4} }). \color{blue}{4} \\\Leftrightarrow & 100x \color{red}{-15} & = & \color{red}{28x} +7 \\\Leftrightarrow & 100x \color{red}{-15} \color{blue}{+15} \color{blue}{-28x} & = & \color{red}{28x} +7 \color{blue}{-28x} \color{blue}{+15} \\\Leftrightarrow & 100x-28x& = & 7+15 \\\Leftrightarrow & \color{red}{72} x& = & 22 \\\Leftrightarrow & x = \frac{22}{72} & & \\\Leftrightarrow & x = \frac{11}{36} & & \\ & V = \left\{ \frac{11}{36} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-2x+\frac{5}{2})& = & 7x+\frac{10}{9} \\\Leftrightarrow & -10x+\frac{25}{2}& = & 7x+\frac{10}{9} \\ & & & \text{kgv van noemers 2 en 9 is 18} \\\Leftrightarrow & \color{blue}{18} .(\frac{-180}{ \color{blue}{18} }x+ \frac{225}{ \color{blue}{18} })& = & (\frac{126}{ \color{blue}{18} }x+ \frac{20}{ \color{blue}{18} }). \color{blue}{18} \\\Leftrightarrow & -180x \color{red}{+225} & = & \color{red}{126x} +20 \\\Leftrightarrow & -180x \color{red}{+225} \color{blue}{-225} \color{blue}{-126x} & = & \color{red}{126x} +20 \color{blue}{-126x} \color{blue}{-225} \\\Leftrightarrow & -180x-126x& = & 20-225 \\\Leftrightarrow & \color{red}{-306} x& = & -205 \\\Leftrightarrow & x = \frac{-205}{-306} & & \\\Leftrightarrow & x = \frac{205}{306} & & \\ & V = \left\{ \frac{205}{306} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-4x+\frac{5}{9})& = & -8x+\frac{10}{3} \\\Leftrightarrow & -28x+\frac{35}{9}& = & -8x+\frac{10}{3} \\ & & & \text{kgv van noemers 9 en 3 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{-252}{ \color{blue}{9} }x+ \frac{35}{ \color{blue}{9} })& = & (\frac{-72}{ \color{blue}{9} }x+ \frac{30}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & -252x \color{red}{+35} & = & \color{red}{-72x} +30 \\\Leftrightarrow & -252x \color{red}{+35} \color{blue}{-35} \color{blue}{+72x} & = & \color{red}{-72x} +30 \color{blue}{+72x} \color{blue}{-35} \\\Leftrightarrow & -252x+72x& = & 30-35 \\\Leftrightarrow & \color{red}{-180} x& = & -5 \\\Leftrightarrow & x = \frac{-5}{-180} & & \\\Leftrightarrow & x = \frac{1}{36} & & \\ & V = \left\{ \frac{1}{36} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{5} (-4x+\frac{4}{7})& = & 9x+\frac{3}{2} \\\Leftrightarrow & -20x+\frac{20}{7}& = & 9x+\frac{3}{2} \\ & & & \text{kgv van noemers 7 en 2 is 14} \\\Leftrightarrow & \color{blue}{14} .(\frac{-280}{ \color{blue}{14} }x+ \frac{40}{ \color{blue}{14} })& = & (\frac{126}{ \color{blue}{14} }x+ \frac{21}{ \color{blue}{14} }). \color{blue}{14} \\\Leftrightarrow & -280x \color{red}{+40} & = & \color{red}{126x} +21 \\\Leftrightarrow & -280x \color{red}{+40} \color{blue}{-40} \color{blue}{-126x} & = & \color{red}{126x} +21 \color{blue}{-126x} \color{blue}{-40} \\\Leftrightarrow & -280x-126x& = & 21-40 \\\Leftrightarrow & \color{red}{-406} x& = & -19 \\\Leftrightarrow & x = \frac{-19}{-406} & & \\\Leftrightarrow & x = \frac{19}{406} & & \\ & V = \left\{ \frac{19}{406} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{2} (-5x+\frac{2}{3})& = & -7x+\frac{7}{3} \\\Leftrightarrow & -10x+\frac{4}{3}& = & -7x+\frac{7}{3} \\ & & & \text{kgv van noemers 3 en 3 is 3} \\\Leftrightarrow & \color{blue}{3} .(\frac{-30}{ \color{blue}{3} }x+ \frac{4}{ \color{blue}{3} })& = & (\frac{-21}{ \color{blue}{3} }x+ \frac{7}{ \color{blue}{3} }). \color{blue}{3} \\\Leftrightarrow & -30x \color{red}{+4} & = & \color{red}{-21x} +7 \\\Leftrightarrow & -30x \color{red}{+4} \color{blue}{-4} \color{blue}{+21x} & = & \color{red}{-21x} +7 \color{blue}{+21x} \color{blue}{-4} \\\Leftrightarrow & -30x+21x& = & 7-4 \\\Leftrightarrow & \color{red}{-9} x& = & 3 \\\Leftrightarrow & x = \frac{3}{-9} & & \\\Leftrightarrow & x = \frac{-1}{3} & & \\ & V = \left\{ \frac{-1}{3} \right\} & \\\end{align}\)