Vgln. eerste graad (reeks 5)

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Alles samen. Gebruik stappenplan en ZRM!

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

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Alles samen. Gebruik stappenplan en ZRM!

Verbetersleutel

1. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (2x-\frac{4}{9})& = & 9x+\frac{5}{9} \\\Leftrightarrow & 14x-\frac{28}{9}& = & 9x+\frac{5}{9} \\ & & & \text{kgv van noemers 9 en 9 is 9} \\\Leftrightarrow & \color{blue}{9} .(\frac{126}{ \color{blue}{9} }x- \frac{28}{ \color{blue}{9} })& = & (\frac{81}{ \color{blue}{9} }x+ \frac{5}{ \color{blue}{9} }). \color{blue}{9} \\\Leftrightarrow & 126x \color{red}{-28} & = & \color{red}{81x} +5 \\\Leftrightarrow & 126x \color{red}{-28} \color{blue}{+28} \color{blue}{-81x} & = & \color{red}{81x} +5 \color{blue}{-81x} \color{blue}{+28} \\\Leftrightarrow & 126x-81x& = & 5+28 \\\Leftrightarrow & \color{red}{45} x& = & 33 \\\Leftrightarrow & x = \frac{33}{45} & & \\\Leftrightarrow & x = \frac{11}{15} & & \\ & V = \left\{ \frac{11}{15} \right\} & \\\end{align}\)
2. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-2} (4x+\frac{4}{3})& = & 3x+\frac{2}{7} \\\Leftrightarrow & -8x-\frac{8}{3}& = & 3x+\frac{2}{7} \\ & & & \text{kgv van noemers 3 en 7 is 21} \\\Leftrightarrow & \color{blue}{21} .(\frac{-168}{ \color{blue}{21} }x- \frac{56}{ \color{blue}{21} })& = & (\frac{63}{ \color{blue}{21} }x+ \frac{6}{ \color{blue}{21} }). \color{blue}{21} \\\Leftrightarrow & -168x \color{red}{-56} & = & \color{red}{63x} +6 \\\Leftrightarrow & -168x \color{red}{-56} \color{blue}{+56} \color{blue}{-63x} & = & \color{red}{63x} +6 \color{blue}{-63x} \color{blue}{+56} \\\Leftrightarrow & -168x-63x& = & 6+56 \\\Leftrightarrow & \color{red}{-231} x& = & 62 \\\Leftrightarrow & x = \frac{62}{-231} & & \\\Leftrightarrow & x = \frac{-62}{231} & & \\ & V = \left\{ \frac{-62}{231} \right\} & \\\end{align}\)
3. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-7} (4x-2)& = & 8x+\frac{4}{5} \\\Leftrightarrow & -28x+14& = & 8x+\frac{4}{5} \\ & & & \text{kgv van noemers 1 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{-140}{ \color{blue}{5} }x+ \frac{70}{ \color{blue}{5} })& = & (\frac{40}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & -140x \color{red}{+70} & = & \color{red}{40x} +4 \\\Leftrightarrow & -140x \color{red}{+70} \color{blue}{-70} \color{blue}{-40x} & = & \color{red}{40x} +4 \color{blue}{-40x} \color{blue}{-70} \\\Leftrightarrow & -140x-40x& = & 4-70 \\\Leftrightarrow & \color{red}{-180} x& = & -66 \\\Leftrightarrow & x = \frac{-66}{-180} & & \\\Leftrightarrow & x = \frac{11}{30} & & \\ & V = \left\{ \frac{11}{30} \right\} & \\\end{align}\)
4. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-6} (3x-\frac{5}{7})& = & -8x+\frac{7}{9} \\\Leftrightarrow & -18x+\frac{30}{7}& = & -8x+\frac{7}{9} \\ & & & \text{kgv van noemers 7 en 9 is 63} \\\Leftrightarrow & \color{blue}{63} .(\frac{-1134}{ \color{blue}{63} }x+ \frac{270}{ \color{blue}{63} })& = & (\frac{-504}{ \color{blue}{63} }x+ \frac{49}{ \color{blue}{63} }). \color{blue}{63} \\\Leftrightarrow & -1134x \color{red}{+270} & = & \color{red}{-504x} +49 \\\Leftrightarrow & -1134x \color{red}{+270} \color{blue}{-270} \color{blue}{+504x} & = & \color{red}{-504x} +49 \color{blue}{+504x} \color{blue}{-270} \\\Leftrightarrow & -1134x+504x& = & 49-270 \\\Leftrightarrow & \color{red}{-630} x& = & -221 \\\Leftrightarrow & x = \frac{-221}{-630} & & \\\Leftrightarrow & x = \frac{221}{630} & & \\ & V = \left\{ \frac{221}{630} \right\} & \\\end{align}\)
5. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{7} (-5x+\frac{3}{10})& = & -9x+\frac{8}{11} \\\Leftrightarrow & -35x+\frac{21}{10}& = & -9x+\frac{8}{11} \\ & & & \text{kgv van noemers 10 en 11 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-3850}{ \color{blue}{110} }x+ \frac{231}{ \color{blue}{110} })& = & (\frac{-990}{ \color{blue}{110} }x+ \frac{80}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -3850x \color{red}{+231} & = & \color{red}{-990x} +80 \\\Leftrightarrow & -3850x \color{red}{+231} \color{blue}{-231} \color{blue}{+990x} & = & \color{red}{-990x} +80 \color{blue}{+990x} \color{blue}{-231} \\\Leftrightarrow & -3850x+990x& = & 80-231 \\\Leftrightarrow & \color{red}{-2860} x& = & -151 \\\Leftrightarrow & x = \frac{-151}{-2860} & & \\\Leftrightarrow & x = \frac{151}{2860} & & \\ & V = \left\{ \frac{151}{2860} \right\} & \\\end{align}\)
6. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (2x-\frac{3}{5})& = & 5x+\frac{10}{7} \\\Leftrightarrow & 8x-\frac{12}{5}& = & 5x+\frac{10}{7} \\ & & & \text{kgv van noemers 5 en 7 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{280}{ \color{blue}{35} }x- \frac{84}{ \color{blue}{35} })& = & (\frac{175}{ \color{blue}{35} }x+ \frac{50}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & 280x \color{red}{-84} & = & \color{red}{175x} +50 \\\Leftrightarrow & 280x \color{red}{-84} \color{blue}{+84} \color{blue}{-175x} & = & \color{red}{175x} +50 \color{blue}{-175x} \color{blue}{+84} \\\Leftrightarrow & 280x-175x& = & 50+84 \\\Leftrightarrow & \color{red}{105} x& = & 134 \\\Leftrightarrow & x = \frac{134}{105} & & \\ & V = \left\{ \frac{134}{105} \right\} & \\\end{align}\)
7. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{-5} (-2x-\frac{5}{11})& = & -7x+\frac{3}{11} \\\Leftrightarrow & 10x+\frac{25}{11}& = & -7x+\frac{3}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{110}{ \color{blue}{11} }x+ \frac{25}{ \color{blue}{11} })& = & (\frac{-77}{ \color{blue}{11} }x+ \frac{3}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 110x \color{red}{+25} & = & \color{red}{-77x} +3 \\\Leftrightarrow & 110x \color{red}{+25} \color{blue}{-25} \color{blue}{+77x} & = & \color{red}{-77x} +3 \color{blue}{+77x} \color{blue}{-25} \\\Leftrightarrow & 110x+77x& = & 3-25 \\\Leftrightarrow & \color{red}{187} x& = & -22 \\\Leftrightarrow & x = \frac{-22}{187} & & \\\Leftrightarrow & x = \frac{-2}{17} & & \\ & V = \left\{ \frac{-2}{17} \right\} & \\\end{align}\)
8. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (-3x-\frac{3}{11})& = & 5x+\frac{3}{10} \\\Leftrightarrow & -12x-\frac{12}{11}& = & 5x+\frac{3}{10} \\ & & & \text{kgv van noemers 11 en 10 is 110} \\\Leftrightarrow & \color{blue}{110} .(\frac{-1320}{ \color{blue}{110} }x- \frac{120}{ \color{blue}{110} })& = & (\frac{550}{ \color{blue}{110} }x+ \frac{33}{ \color{blue}{110} }). \color{blue}{110} \\\Leftrightarrow & -1320x \color{red}{-120} & = & \color{red}{550x} +33 \\\Leftrightarrow & -1320x \color{red}{-120} \color{blue}{+120} \color{blue}{-550x} & = & \color{red}{550x} +33 \color{blue}{-550x} \color{blue}{+120} \\\Leftrightarrow & -1320x-550x& = & 33+120 \\\Leftrightarrow & \color{red}{-1870} x& = & 153 \\\Leftrightarrow & x = \frac{153}{-1870} & & \\\Leftrightarrow & x = \frac{-9}{110} & & \\ & V = \left\{ \frac{-9}{110} \right\} & \\\end{align}\)
9. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (3x+\frac{5}{11})& = & 2x+\frac{8}{11} \\\Leftrightarrow & 9x+\frac{15}{11}& = & 2x+\frac{8}{11} \\ & & & \text{kgv van noemers 11 en 11 is 11} \\\Leftrightarrow & \color{blue}{11} .(\frac{99}{ \color{blue}{11} }x+ \frac{15}{ \color{blue}{11} })& = & (\frac{22}{ \color{blue}{11} }x+ \frac{8}{ \color{blue}{11} }). \color{blue}{11} \\\Leftrightarrow & 99x \color{red}{+15} & = & \color{red}{22x} +8 \\\Leftrightarrow & 99x \color{red}{+15} \color{blue}{-15} \color{blue}{-22x} & = & \color{red}{22x} +8 \color{blue}{-22x} \color{blue}{-15} \\\Leftrightarrow & 99x-22x& = & 8-15 \\\Leftrightarrow & \color{red}{77} x& = & -7 \\\Leftrightarrow & x = \frac{-7}{77} & & \\\Leftrightarrow & x = \frac{-1}{11} & & \\ & V = \left\{ \frac{-1}{11} \right\} & \\\end{align}\)
10. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (-4x+\frac{4}{7})& = & -5x+\frac{3}{5} \\\Leftrightarrow & -12x+\frac{12}{7}& = & -5x+\frac{3}{5} \\ & & & \text{kgv van noemers 7 en 5 is 35} \\\Leftrightarrow & \color{blue}{35} .(\frac{-420}{ \color{blue}{35} }x+ \frac{60}{ \color{blue}{35} })& = & (\frac{-175}{ \color{blue}{35} }x+ \frac{21}{ \color{blue}{35} }). \color{blue}{35} \\\Leftrightarrow & -420x \color{red}{+60} & = & \color{red}{-175x} +21 \\\Leftrightarrow & -420x \color{red}{+60} \color{blue}{-60} \color{blue}{+175x} & = & \color{red}{-175x} +21 \color{blue}{+175x} \color{blue}{-60} \\\Leftrightarrow & -420x+175x& = & 21-60 \\\Leftrightarrow & \color{red}{-245} x& = & -39 \\\Leftrightarrow & x = \frac{-39}{-245} & & \\\Leftrightarrow & x = \frac{39}{245} & & \\ & V = \left\{ \frac{39}{245} \right\} & \\\end{align}\)
11. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{4} (5x-\frac{3}{5})& = & -3x+\frac{4}{5} \\\Leftrightarrow & 20x-\frac{12}{5}& = & -3x+\frac{4}{5} \\ & & & \text{kgv van noemers 5 en 5 is 5} \\\Leftrightarrow & \color{blue}{5} .(\frac{100}{ \color{blue}{5} }x- \frac{12}{ \color{blue}{5} })& = & (\frac{-15}{ \color{blue}{5} }x+ \frac{4}{ \color{blue}{5} }). \color{blue}{5} \\\Leftrightarrow & 100x \color{red}{-12} & = & \color{red}{-15x} +4 \\\Leftrightarrow & 100x \color{red}{-12} \color{blue}{+12} \color{blue}{+15x} & = & \color{red}{-15x} +4 \color{blue}{+15x} \color{blue}{+12} \\\Leftrightarrow & 100x+15x& = & 4+12 \\\Leftrightarrow & \color{red}{115} x& = & 16 \\\Leftrightarrow & x = \frac{16}{115} & & \\ & V = \left\{ \frac{16}{115} \right\} & \\\end{align}\)
12. \(\text{(1) Haakjes (2) Breuken weg (3) + - (4) . /} \\ \begin{align} & \color{red}{3} (5x-\frac{5}{4})& = & -4x+\frac{4}{7} \\\Leftrightarrow & 15x-\frac{15}{4}& = & -4x+\frac{4}{7} \\ & & & \text{kgv van noemers 4 en 7 is 28} \\\Leftrightarrow & \color{blue}{28} .(\frac{420}{ \color{blue}{28} }x- \frac{105}{ \color{blue}{28} })& = & (\frac{-112}{ \color{blue}{28} }x+ \frac{16}{ \color{blue}{28} }). \color{blue}{28} \\\Leftrightarrow & 420x \color{red}{-105} & = & \color{red}{-112x} +16 \\\Leftrightarrow & 420x \color{red}{-105} \color{blue}{+105} \color{blue}{+112x} & = & \color{red}{-112x} +16 \color{blue}{+112x} \color{blue}{+105} \\\Leftrightarrow & 420x+112x& = & 16+105 \\\Leftrightarrow & \color{red}{532} x& = & 121 \\\Leftrightarrow & x = \frac{121}{532} & & \\ & V = \left\{ \frac{121}{532} \right\} & \\\end{align}\)